Causal set theory bibliography

"Main article: Causal Sets"

This Causal Set Theory Bibliography is intended to aid causal set research. It gathers together academic papers, books, talks and PhD theses related to causal set theory and is intended to help readers find references which are often difficult to locate. Items are classified into sections based on their primary topic.

Reviews

*L. Bombelli, " [http://www.gravity.psu.edu/events/conferences/Quantum_GravityIII/proceedings.shtml Causal Sets: Overview and Status] ", Talk given at Quantum Gravity in the Americas III, August 24-26, 2006; (Introduction, Overview)

*F. Dowker, "Causal sets and the deep structure of spacetime", ; (Introduction)
*J. Henson, "The causal set approach to quantum gravity", ; (Introduction, Overview)

*R.D. Sorkin, "Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)", In Proceedings of the Valdivia Summer School, edited by A. Gomberoff and D. Marolf; ; (Introduction, Glossary)

*R.D. Sorkin, " [http://www.einstein-online.info/en/spotlights/causal_sets/ Geometry from order: causal sets] ", Non-technical article for [http://www.einstein-online.info Einstein Online]

Foundations

*L. Bombelli, J. Lee, D. Meyer, R.D. Sorkin, " [http://prola.aps.org/abstract/PRL/v59/i5/p521_1 Spacetime as a causal set] ", Phys. Rev. Lett. 59:521-524 (1987) ; (Introduction, Foundations)

*C. Moore, " [http://link.aps.org/abstract/PRL/v60/p655 Comment on "Space-time as a causal set"] ", Phys. Rev. Lett. 60, 655 (1988); (Foundations)

*L. Bombelli, J. Lee, D. Meyer, R.D. Sorkin, " [http://link.aps.org/abstract/PRL/v60/p656 Bombelli et al. Reply] ", Phys. Rev. Lett. 60, 656 (1988); (Foundations)
*L. Bombelli, "Space-time as a Causal Set", PhD thesis (Syracuse University, 1987); (Introduction)

*D. Finkelstein, " [http://prola.aps.org/abstract/PR/v184/i5/p1261_1 Space-time code] ", Phys. Rev. 184:1261 (1969); (Foundations)

*D. Finkelstein, " [http://dx.doi.org/10.1007/BF00669395 "Superconducting" Causal Nets] ", Int. J. Th. Phys 27:473(1988); (Foundations)

*J. Myrheim, " [http://doc.cern.ch//archive/electronic/kek-scan//197808143.pdf Statistical geometry] ", CERN preprint TH-2538 (1978); (Foundations, Historical)

*R.D. Sorkin, "Does a Discrete Order underly Spacetime and its Metric?", Proceedings of the Third Canadian Conference on General Relativity and Relativistic Astrophysics, (Victoria, Canada, May, 1989), edited by A. Coley, F. Cooperstock, B.Tupper, pp. 82-86, (World Scientific, 1990); (Introduction)

*R.D. Sorkin, " [http://physics.syr.edu/~sorkin/some.papers/ First Steps with Causal Sets] ", General Relativity and Gravitational Physics, (Proceedings of the Ninth Italian Conference of the same name, held Capri, Italy, September, 1990), 68-90, (World Scientific, Singapore), (1991), R. Cianci, R. de Ritis, M. Francaviglia, G. Marmo, C. Rubano, P. Scudellaro (eds.); (Introduction)

*R.D. Sorkin, " [http://physics.syr.edu/~sorkin/some.papers/ Spacetime and Causal Sets] ", Relativity and Gravitation: Classical and Quantum, (Proceedings of the SILARG VII Conference, held Cocoyoc, Mexico, December, 1990), pages 150-173, (World Scientific, Singapore, 1991), J.C. D’Olivo, E. Nahmad-Achar, M.Rosenbaum, M.P. Ryan, L.F. Urrutia and F. Zertuche (eds.); (Introduction)

*R.D. Sorkin, "Forks in the Road, on the Way to Quantum Gravity", Talk given at the conference entitled “Directions in General Relativity”, held at College Park, Maryland, May, 1993, Int. J. Th. Phys. 36: 2759–2781 (1997); ; (Philosophical, Introduction)

Historical

*A. Einstein, "Letter to H.S. Joachim", August 14, 1954; Item 13-453 cited in J. Stachel,“Einstein and the Quantum: Fifty Years of Struggle”, in From Quarks to Quasars,Philosophical Problems of Modern Physics, edited by R.G. Colodny (U. Pittsburgh Press, 1986), pages 380-381; (Historical)

*G.'t Hooft, "Quantum gravity: a fundamental problem and some radical ideas", Recent Developments in Gravitation (Proceedings of the 1978 Cargese Summer Institute) edited by M. Levy and S. Deser (Plenum, 1979); (Introduction, Foundations, Historical)

*B. Riemann, " [http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/ Uber die Hypothesen, welche der Geometrie zu Grunde liegen] ", The Collected Works of B. Riemann (Dover NY 1953); ; (Historical)

*R.D. Sorkin, "A Specimen of Theory Construction from Quantum Gravity", The Creation of Ideas in Physics: Studies for a Methodology of Theory Construction (Proceedings of the Thirteenth Annual Symposium in Philosophy, held Greensboro, North Carolina, March, 1989) pp. 167-179 (Number 55 in the University of Western Ontario Series in Philosophy of Science) (Kluwer Academic Publishers, Dordrecht, 1995) J. Leplin (ed.); ; (Philosophical, Historical)

* E.C. Zeeman, " [http://link.aip.org/link/?JMAPAQ/5/490/1 Causality Implies the Lorentz Group] ", J. Math. Phys. 5: 490-493; (Historical, Foundations)

General

*H. Reichenbach; ;Physikal. Zeitschr. 22:683 (1921);;

*H. Reichenbach; "Axiomatik der relativistische Raum-Zeit-Lehre" (translated into English as Axiomatization of the theory of relativity); Berkeley, University of California Press, 1969;;

*D.D. Reid; "Introduction to causal sets: an alternate view of spacetime structure"; Canadian Journal of Physics 79, 1-16 (2001); ; (General);

*R.D. Sorkin; " [http://www.maths.qmw.ac.uk/~pjc/csgnotes/ Causal set glossary and bibliography] " (20 November 2001); (Glossary and bibliography);

*R.D. Sorkin " [http://pirsa.org/05090001 Is a past-finite causal order the inner basis of spacetime?] " Talk given at Perimeter Institute 07/09/2005

Manifoldness

*L. Bombelli, D.A. Meyer; " [http://dx.doi.org/10.1016/0375-9601(89)90474-X The origin of Lorentzian geometry] "; Phys. Lett. A 141:226-228 (1989); (Manifoldness)

*L. Bombelli, R.D. Sorkin, "When are Two Lorentzian Metrics close?", General Relativity and Gravitation, proceedings of the 12th International Conference on General Relativity and Gravitation, held July 2-8, 1989, in Boulder, Colorado, USA, under the auspices of the International Society on General Relativity and Gravitation, 1989, p.220; (Closeness of Lorentzian manifolds)

*L. Bombelli, "Causal sets and the closeness of Lorentzian manifolds", Relativity in General: proceedings of the Relativity Meeting "93, held September 7-10, 1993, in Salas, Asturias, Spain. Edited by J. Diaz Alonso, M. Lorente Paramo. ISBN 2-86332-168-4. Published by Editions Frontieres, 91192 Gif-sur-Yvette Cedex, France, 1994, p. 249; (Closeness of Lorentzian manifolds)

*L. Bombelli, "Statistical Lorentzian geometry and the closeness of Lorentzian manifolds", J. Math. Phys.41:6944-6958 (2000); (Closeness of Lorentzian manifolds, Manifoldness)

*A.R. Daughton, " [http://www.iop.org/EJ/abstract/0264-9381/15/11/009 An investigation of the symmetric case of when causal sets can embed into manifolds] ", Class. Quant. Grav.15(11):3427-3434 (Nov,1998); (Manifoldness)

*J. Henson, "Constructing an interval of Minkowski space from a causal set", Class.Quant.Grav. 23 (2006) L29-L35; ; (Continuum limit, Sprinkling)

*S. Major, D.P. Rideout, S. Surya, "On Recovering Continuum Topology from a Causal Set", J.Math.Phys.48:032501,2007; (Continuum Topology)

*D.A. Meyer, " [http://hdl.handle.net/1721.1/14328 The Dimension of Causal Sets] ", PhD thesis (M.I.T., 1988); (Dimension theory)

*D.A. Meyer, "The Dimension of Causal Sets I: Minkowski dimension", Syracuse University preprint (1988); (Dimension theory)

*D.A. Meyer, "The Dimension of Causal Sets II: Hausdorff dimension" ,Syracuse University preprint (1988); (Dimension theory)

*D.A. Meyer, " [http://dx.doi.org/10.1007/BF01110544 Spherical containment and the Minkowski dimension of partial orders] ", Order 10: 227-237 (1993); (Dimension theory)

*J. Noldus, " [http://dx.doi.org/10.1088/0264-9381/19/23/313 A new topology on the space of Lorentzian metrics on a fixed manifold] ", Class. Quant. Grav 19: 6075-6107 (2002); (Closeness of Lorentzian manifolds)

*J. Noldus, " [http://dx.doi.org/10.1088/0264-9381/21/4/007 A Lorentzian Gromov–Hausdorff notion of distance] ", Class. Quant. Grav. 21, 839-850, (2004); (Closeness of Lorentzian manifolds)

*D.D. Reid, "Manifold dimension of a causal set: Tests in conformally flat spacetimes", Phys.Rev. D67 (2003) 024034; (Dimension theory)

*R.D. Sorkin; " [http://dx.doi.org/10.1007/BF00673986 A Finitary Substitute for Continuous Topology] ", Int. J. Theor. Phys. 30 7: 923-947 (1991); (Foundational)

*R.D. Sorkin, "Posets as Lattice Topologies", General Relativity and Gravitation, vol. I, 635-637 (Roma, Consiglio Nazionale Delle Ricerche, 1983), B. Bertotti, F. de Felice, A. Pascolini (eds.); (Topology)

*S. Surya, "Causal Set Topology";

Cosmological Constant

*M. Ahmed, S. Dodelson, P.B. Greene, R.D. Sorkin, "Everpresent lambda"; Phys. Rev. D69, 103523, (2004) ; (Cosmological Constant)

*Y. Jack Ng and H. van Dam, "A small but nonzero cosmological constant"; Int. J. Mod. Phys D. 10 : 49 (2001) ; (PreObservation Cosmological Constant)

*Y. Kuznetsov, "On cosmological constant in Causal Set theory";

*R.D. Sorkin, "A Modified Sum-Over-Histories for Gravity"; reported in Highlights in gravitation and cosmology: Proceedings of the International Conference on Gravitation and Cosmology, Goa, India, 14-19 December, 1987, edited by B. R. Iyer, Ajit Kembhavi, Jayant V. Narlikar, and C. V. Vishveshwara, see pages 184-186 in the article by D. Brill and L. Smolin: “Workshop on quantum gravity and new directions”, pp 183-191 (Cambridge University Press, Cambridge, 1988); (PreObservation Cosmological Constant)

*R.D. Sorkin; " [http://dx.doi.org/10.1007/BF00670514 On the Role of Time in the Sum-over-histories Framework for Gravity] ", paper presented to the conference on The History of Modern Gauge Theories, held Logan, Utah, July 1987; Int. J. Theor. Phys. 33 : 523-534 (1994); (PreObservation Cosmological Constant)

*R.D. Sorkin, " [http://physics.syr.edu/~sorkin/some.papers/ First Steps with Causal Sets] ", in R. Cianci, R. de Ritis, M. Francaviglia, G. Marmo, C. Rubano, P. Scudellaro (eds.), General Relativity and Gravitational Physics (Proceedings of the Ninth Italian Conference of the same name, held Capri, Italy, September, 1990), pp. 68-90 (World Scientific, Singapore, 1991); (PreObservation Cosmological Constant)

*R.D. Sorkin; "Forks in the Road, on the Way to Quantum Gravity", talk given at the conference entitled “Directions in General Relativity”, held at College Park, Maryland, May, 1993; Int. J. Th. Phys. 36 : 2759–2781 (1997) ; (PreObservation Cosmological Constant)

*R.D. Sorkin, "Discrete Gravity"; a series of lectures to the First Workshop on Mathematical Physics and Gravitation, held Oaxtepec, Mexico, Dec. 1995 (unpublished); (PreObservation Cosmological Constant)

*R.D. Sorkin, "Big extra dimensions make Lambda too small"; ; (Cosmological Constant)

*R.D. Sorkin, "Is the cosmological "constant" a nonlocal quantum residue of discreteness of the causal set type?"; Proceedings of the PASCOS-07 Conference, July 2007, Imperial College London; ; (Cosmological Constant)

Lorentz and Poincaré Invariance, Phenomenology

*L. Bombelli, J. Henson, R.D. Sorkin; "Discreteness without symmetry breaking: a theorem"; ; (Lorentz invariance, Sprinkling)

*F. Dowker, J. Henson, R.D. Sorkin, "Quantum gravity phenomenology, Lorentz invariance and discreteness"; Mod. Phys. Lett. A19, 1829–1840, (2004) ; (Lorentz invariance, Phenomenology)

*F. Dowker, " [http://loops05.aei.mpg.de/index_files/PDF_Files/dowker.pdf Causal Set Phenomenology] "; Talk given at Loops 05, 10-14 October 2005, Potsdam, Max Planck Institute for Gravitational Physics

*J. Henson, "Macroscopic observables and Lorentz violation in discrete quantum gravity"; ; (Lorentz invariance, Phenomenology)

*N. Kaloper, D. Mattingly, "Low energy bounds on Poincaré violation in causal set theory"; Phys. Rev. D 74, 106001 (2006) (Poincaré invariance, Phenomenology)

*D. Mattingly, "Causal sets and conservation laws in tests of Lorentz symmetry"; Phys. Rev. D 77, 125021 (2008) (Lorentz invariance, Phenomenology)

*J. Scargle, " [http://scipp.ucsc.edu/seminars/experimental/archive_sq07/scargle_4-24-07.ppt Testing Quantum Gravity Theories with GLAST] "; Talk given at Santa Cruz Institute for Particle Physics, April 24 2007. (Lorentz invariance, Phenomenology)

*J. Zuntz, "The CMB in a Causal Set Universe",

Black Hole Entropy

*D. Dou, "Causal Sets, a Possible Interpretation for the Black Hole Entropy, and Related Topics"; PhD thesis (SISSA, Trieste, 1999); (Black hole entropy)

*D. Dou, "Black Hole Entropy as Causal Links"; Fnd. of Phys, 33 2:279-296(18) (2003); (Black hole entropy)

*G.'t Hooft, " [http://igitur-archive.library.uu.nl/phys/2005-0622-153848/14549.pdf On the quantum structure of a black hole] "; Nuclear Phys. B 256:727-745 (1985); ; (Black hole entropy)

*D.P. Rideout, S. Zohren, "Counting entropy in causal set quantum gravity" ; ; (Black hole entropy)

*D.P. Rideout, S. Zohren, "Evidence for an entropy bound from fundamentally discrete gravity"; Class.Quant.Grav. 23 (2006) 6195-6213; (Black hole entropy)

*R.D. Sorkin, "On the Entropy of the Vacuum Outside a Horizon"; Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, pp. 734-736 (Roma, Consiglio Nazionale Delle Ricerche, 1983), B. Bertotti, F. de Felice and A. Pascolini (eds.); (Black hole entropy)

Quantum Measure

*J. Henson, " [http://pirsa.org/06120039 A Bell inequality Analogue in quantum measure theory] " Talk given at Perimeter Institute 7/12/2006

*X. Martin, D. O'Connor, R.D. Sorkin; "The Random walk in generalized quantum theory"; Phys.Rev.D71:024029,2005; (Quantum Measure Theory)

*R.B. Salgado; "Some Identities for the Quantum Measure and its Generalizations"; ; (Quantum Measure Theory)

*R.D. Sorkin; "Quantum mechanics as quantum measure theory"; Mod.Phys.Lett.A9:3119-3128,1994; (Quantum Measure Theory)

*R.D. Sorkin; "Quantum measure theory and its interpretation"; 4TH Drexel Symposium on Quantum Nonintegrability, 8-11 Sep 1994, Philadelphia, PA; ; (Quantum Measure Theory)

Locality and Quantum Field Theory

*A.R. Daughton; "The Recovery of Locality for Causal Sets and Related Topics"; PhD thesis (Syracuse University, 1993); (Locality)

*B.Z. Foster, T. Jacobson; "Quantum field theory on a growing lattice"; JHEP08(2004)024 (Quantum field theory)

*S. Johnston; " [http://pirsa.org/08040043/ Particle Propagators from Discrete Spacetime] "; Talk given at Perimeter Institute 14/04/2008 (Quantum field theory)

*S. Johnston; "Particle propagators on discrete spacetime"; 2008 Class. Quantum Grav. 25 202001; (Quantum Field Theory)

*R.D. Sorkin; "Does Locality Fail at Intermediate Length-Scales"; Towards Quantum Gravity, Daniele Oriti (ed.) (Cambridge University Press, 2007); ; (d'Alembertian, Locality)

*R.D. Sorkin; " [http://pirsa.org/07010001 Does quantum gravity give rise to an observable nonlocality?] "; Talk given at Perimeter Institute 17/01/2007 (d'Alembertian, Locality)

*R. Sverdlov; " [http://pirsa.org/08020043/ Introduction of bosonic fields into causal set theory] "; Talk given at Perimeter Institute 19/02/2008 (Quantum field theory)

*R. Sverdlov, L. Bombelli; "Gravity and Matter in Causal Set Theory";

*R. Sverdlov; "A Geometrical Description of Spinor Fields";

*R. Sverdlov; "Bosonic Fields in Causal Set Theory";

*R. Sverdlov; "Gauge Fields in Causal Set Theory";

*R. Sverdlov; "Spinor fields in Causal Set Theory";

Dynamics

*A.Ash, P. McDonald, "Moment Problems and the Causal Set Approach to Quantum Gravity"; J.Math.Phys. 44 (2003) 1666-1678;

*G. Brightwell, H.F. Dowker, R.S. Garcia, J. Henson, R.D. Sorkin; "General covariance and the "problem of time" in a discrete cosmology"; In ed. K. Bowden, Correlations:Proceedings of the ANPA 23 conference, August 16-21, 2001, Cambridge, England, pp. 1-17. Alternative Natural Philosophy Association, (2002).;; (Cosmology, Dynamics, Observables)

*G. Brightwell, H.F. Dowker, R.S. Garcia, J. Henson, R.D. Sorkin; "Observables" in causal set cosmology"; Phys. Rev. D67, 084031, (2003); ; (Cosmology, Dynamics, Observables)

*G. Brightwell, J. Henson, S. Surya; "A 2D model of Causal Set Quantum Gravity: The emergence of the continuum"; ; (Quantum Dynamics, Toy Model)

*G.Brightwell, N. Georgiou; " [http://www.maths.bris.ac.uk/~maxng/contlim.pdf Continuum limits for classical sequential growth models] " University of Bristol preprint. (Dynamics)

*A. Criscuolo, H. Waelbroeck; "Causal Set Dynamics: A Toy Model"; Class. Quant. Grav.16:1817-1832 (1999); ; (Quantum Dynamics, Toy Model)

*F. Dowker, S. Surya; "Observables in extended percolation models of causal set cosmology";Class. Quant. Grav. 23, 1381-1390 (2006); ; (Cosmology, Dynamics, Observables)

*J. Henson; "Comparing causality principles"; Stud.Hist.Philos.Mod.Phys. 36 (2005) 519-543; ; (Quantum Dynamics, Philosophy)

*A.L. Krugly; " [http://dx.doi.org/10.1023/A:1013273214769 Causal Set Dynamics and Elementary Particles] "; Int. J. Theo. Phys 41 1:1-37(2004);; (Quantum Dynamics)

*S. Major, D.P. Rideout, S. Surya; "Spatial Hypersurfaces in Causal Set Cosmology"; Class.Quant.Grav. 23 (2006) 4743-4752; ; (Observables, Continuum topology)

*A. Mallios, I. Raptis; "Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum Causality"

*F. Markopoulou; "The internal description of a causal set: What the universe looks like from the inside" Commun.Math.Phys. 211 (2000) 559-583

*X. Martin, D. O'Connor, D.P. Rideout, R.D. Sorkin; "On the “renormalization” transformations induced by cycles of expansion and contraction in causal set cosmology"; Phys. Rev. D 63, 084026 (2001); (Cosmology, Dynamics)

*D.A. Meyer; "Spacetime Ising models"; (UCSD preprint May 1993); (Quantum Dynamics)

*D.A. Meyer; " [http://dx.doi.org/10.1007/BF00759191 Why do clocks tick?] "; General Relativity and Gravitation 25 9:893-900;; (Quantum Dynamics)

*D.A. Meyer; Talk given at the 1997 Santa Fe workshop: " [http://t8web.lanl.gov/people/emil/Slides/sf97talks.html Causal Sets and Feynman diagrams] "; Presented at "New Directions in Simplicial Quantum Gravity" July 28 - August 8, 1997; (Feynman diagrams, Quantum Dynamics)

*I. Raptis; "Quantum Space-Time as a Quantum Causal Set",

*I. Raptis; "Algebraic Quantization of Causal Sets"; Int.J.Theor.Phys 39:1233-1240,2000; ; (Algebraic quantization);

*D.P.Rideout, R.D. Sorkin; "A classical sequential growth dynamics for causal sets", Phys. Rev D, 6, 024002 (2000); (Cosmology, Dynamics)

*D.P. Rideout, R.D. Sorkin; "Evidence for a continuum limit in causal set dynamics" Phys.Rev.D63:104011,2001; (Cosmology, Dynamics)

*D.P. Rideout; "Dynamics of Causal Sets"; PhD Thesis (Syracuse University 2001); ; (Cosmology, Dynamics)

*R.D. Sorkin; "Indications of causal set cosmology"; Int. J. Theor. Ph. 39(7):1731-1736 (2000); ; (Cosmology, Dynamics)

*R.D. Sorkin; "Relativity theory does not imply that the future already exists: a counterexample"; Relativity and the Dimensionality of the World, Vesselin Petkov (ed.) (Springer 2007, in press); ; (Dynamics, Philosophy)

*R.D. Sorkin; Two Talks given at the 1997 Santa Fe workshop: " [http://t8web.lanl.gov/people/emil/Slides/sf97talks.html A Review of the Causal Set Approach to Quantum Gravity] " and " [http://t8web.lanl.gov/people/emil/Slides/sf97talks.html A Growth Dynamics for Causal Sets] "; Presented at ”New Directions in Simplicial Quantum Gravity” July 28 - August 8, 1997; ;;

*M. Varadarajan, D.P. Rideout; "A general solution for classical sequential growth dynamics of Causal Sets"; Phys.Rev. D73 (2006) 104021; ; (Cosmology, Dynamics)

Geometry

*G. Brightwell, R. Gregory; " [http://link.aps.org/abstract/PRL/v66/p260 The Structure of Random Discrete Spacetime] "; Phys. Rev. Lett. 66:260-263 (1991); (Geodesic Length)

*G. W. Gibbons, S. N. Solodukhin; "The Geometry of Small Causal Diamonds" (Causal intervals)

*S.W. Hawking, A.R. King, P.J. McCarthy; " [http://link.aip.org/link/?JMAPAQ/17/174/1 A new topology for curved space–time which incorporates the causal, differential, and conformal structures] "; J. Math. Phys. 17 2:174-181 (1976); (Geometry, Causal Structure)

*A.V. Levichev; "Prescribing the conformal geometry of a lorentz manifold by means of its causal structure"; Soviet Math. Dokl. 35:452-455, (1987); (Geometry, Causal Structure)

*D. Malament; " [http://link.aip.org/link/?JMAPAQ/18/1399/1 The class of continuous timelike curves determines the topology of spacetime] "; J. Math. Phys. 18 7:1399-1404 (1977); (Geometry, Causal Structure)

*A.A. Robb; "Geometry of Time and Space"; Cambridge University Press, 1936; (Geometry, Causal Structure)

*R.D. Sorkin, E. Woolgar; "A Causal Order for Spacetimes with C^0 Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves"; Classical & Quantum Gravity 13: 1971-1994 (1996); (Causal Structure)

Poset Theory

*N. Alon, B. Bollobas, G. Brightwell, S. Janson; " [http://links.jstor.org/sici?sici=1050-5164%28199402%294%3A1%3C108%3ALEOARP%3E2.0.CO%3B2-5 Linear extensions of a random partial order] "; Ann. Applied Prob. 4: 108-123 (1994); (Random partial orders);

*B. Bollobas, G. Brightwell; " [http://links.jstor.org/sici?sici=0002-9947%28199103%29324%3A1%3C59%3ABARPO%3E2.0.CO%3B2-Q Box spaces and random partial orders] "; Trans. Amer. Math. Soc 324(1): 59-72 (1991); (Random partial orders);

*B. Bollobas, G. Brightwell; " [http://links.jstor.org/sici?sici=1050-5164%28199211%292%3A4%3C1009%3ATHOARP%3E2.0.CO%3B2-1 The Height of a Random Partial Order: Concentration of Measure] "; Annals of Applied Probability 2: 1009-1018 (1992); (Geodesics);

*B. Bollobas, G. Brightwell; " [http://dx.doi.org/10.1137/S0895480194281215 The structure of random graph orders] "; SIAM J. Discrete Math.10: 318-335 (1997); (Random partial orders);

*B. Bollobas, G. Brightwell; "The dimension of random graph orders"; The Mathematics of Paul Erdos II, R.L. Graham and J. Nesetril, eds. (Springer-Verlag, 1996), pp. 51-69; (Random partial orders);

*B. Bollobas, G. Brightwell; "The width of random graph orders"; Math. Scientist 20: 69-90 (1995); (Random partial orders);

*G. Brightwell; "Models of Random Partial Orders"; Surveys in Combinatorics, 1993, London Math. Soc. Lecture Notes Series 187:53-83, ed. Keith;; (Random partial orders);

*G. Brightwell, P. Winkler; " [http://dx.doi.org/10.1007/BF00563524 Sphere Orders] "; Order 6:235-240 (1989); (Order Theory);

*D. Crippa, K. Simon, P. Trunz; " [http://dx.doi.org/10.1017/S0963548397002964 Markov Processes Involving q-Stirling Numbers] "; Combinatorics, Probability and Computing 6: 165-178 (1997);;;

*D. Dhar; " [http://link.aip.org/link/?JMAPAQ/19/1711/1 Entropy and phase transitions in partially ordered sets] "; J. Math. Phys 19: 1711-1713 (1978); ; (Phase Transitions for Posets, Order Theory);

*D. Dhar; "On phase transitions in posets"; Pacific J. Math. 90: 299-305 (1980); (Phase Transitions for Posets, Order Theory);

*D. Dhar; " [http://projecteuclid.org/euclid.pjm/1102778989 Asymptotic Enumeration of Partially Ordered Sets] "; Pacific J. of Math.90:299 (1980);; (Phase Transitions for Posets, Order Theory);

*S. Felsner, P.C. Fishburn, W.T. Trotter; " [http://dx.doi.org/10.1016/S0012-365X(98)00314-8 Finite three dimensional partial orders which are not sphere orders] "; Discrete Math. 201: 101-132 (1999);;

*J.H. Kim, B. Pittel; " [http://dx.doi.org/10.1006/jctb.2000.1966 On tail distribution of interpost distance] "; J. Combinatorial Theory, B 80 1:49-56 (2000); (Geodesics);

*D.J. Kleitman, B.L. Rothschild; " [http://links.jstor.org/sici?sici=0002-9939%28197006%2925%3A2%3C276%3ATNOFT%3E2.0.CO%3B2-O The Number of Finite Topologies] "; Proc. Amer. Math. Society 25:276-282 (1970); (Order Theory);

*D.J. Kleitman, B.L. Rothschild; " [http://links.jstor.org/sici?sici=0002-9947%28197504%29205%3C205%3AAEOPOO%3E2.0.CO%3B2-W Asymptotic Enumeration of Partial Orders on a Finite Set] "; Trans. Amer. Math. Society 205:205-220 (1975); (Order Theory);

*D.J. Kleitman, B.L. Rothschild; " [http://dx.doi.org/10.1016/0378-4371(79)90212-7 A Phase Transition on Partial Orders] "; Physica 96A:254-259 (1979);; (Phase Transitions for Posets, Order Theory);

*C. M. Newman; " [http://dx.doi.org/10.1002/rsa.3240030304 Chain Lengths in Certain Random Directed Graphs] "; Random Structures and Algorithms 3: 243-253 (1992); ; (Chain lengths);

*B. Pittel, R. Tungol; " [http://dx.doi.org/10.1002/1098-2418(200103)18:2%3C164::AID-RSA1004%3E3.0.CO;2-H A Phase Transition Phenomenon in a Random Directed Acyclic Graph] "; Combinatorics, Probability and Computing 18 2 p164; ; (Phase Transitions, Random partial orders);

*K. Simon, D. Crippa, F. Collenberg; " [http://dx.doi.org/10.1007/3-540-57273-2 On the Distribution of the Transitive Closure in a Random Acyclic Digraph] "; Lecture Notes in Computer Science 726: 345-356 (1993); (Transitive closure, Graph theory);

*K. Simon; " [http://dx.doi.org/10.1016/0304-3975(88)90032-1 Improved Algorithm for Transitive Closure on Acyclic Digraphs] "; Theoretical Computer Science 58 (1988);; (Transitive closure, Graph theory);

*R.D. Sorkin; "Indecomposable Ideals in Incidence Algebras";Mod.Phys.Lett. A18 (2003) 2491-2500;; (Order theory);


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Causal sets — The causal sets programme is an approach to quantum gravity. Its founding principle is that spacetime is fundamentally discrete and that the spacetime points are related by a partial order. This partial order has the physical meaning of the… …   Wikipedia

  • Democratic peace theory — (or liberal democratic theory[1] or simply the democratic peace ) is the theory that democracies, for some appropriate definition of democracy, rarely, or even never, go to war with one another. Some have preferred the term inter democracy… …   Wikipedia

  • Communication theory — is a field of information and mathematics that studies the technical process of information[1] and the human process of human communication.[2] Contents 1 History 1.1 Origins …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Charles Sanders Peirce —  B …   Wikipedia

  • Philosophy of mathematics — The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of …   Wikipedia

  • Sign relation — A sign relation is the basic construct in the theory of signs, also known as semeiotic or semiotics, as developed by Charles Sanders Peirce.AnthesisThus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without… …   Wikipedia

  • Rhetoric — This article is about the art of rhetoric in general. For the work by Aristotle, see Rhetoric (Aristotle). Painting depicting a lecture in a knight academy, painted by Pieter Isaacsz or Reinhold Timm for Rosenborg Castle as part of a series of… …   Wikipedia

  • Speech act — For the US Act, see SPEECH Act of 2010. Speech Act is a technical term in linguistics and the philosophy of language. The contemporary use of the term goes back to John L. Austin s doctrine of locutionary, illocutionary, and perlocutionary acts.… …   Wikipedia

  • A New Kind of Science —   Author(s) Stephen Wolfram Country …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.