User:StevenJohnston/CSBOctober2008

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.

Introduction and Reviews

 * L. Bombelli. Causal Set reference page (Overview)


 * L. Bombelli. 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, gr-qc/0508109; (Introduction)


 * F. Dowker, Causal sets as discrete spacetime, Contemporary Physics, vol. 47, Issue 1, p.1-9; (Overview, Introduction)


 * J. Henson, The causal set approach to quantum gravity, gr-qc/0601121; (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; gr-qc/0309009; (Introduction, Glossary)


 * R.D. Sorkin, Geometry from order: causal sets, Non-technical article for Einstein Online


 * R.D. Sorkin, Some Insights for Quantum Gravity Derived from Work on Causal Sets; Talk given at Loops 05, 10-14 October 2005, Potsdam, Max Planck Institute for Gravitational Physics (Overview)

Foundations

 * L. Bombelli, J. Lee, D. Meyer, R.D. Sorkin, Spacetime as a causal set, Phys. Rev. Lett. 59:521-524 (1987) ; (Introduction, Foundations)


 * C. Moore, Comment on "Space-time as a causal set",  Phys. Rev. Lett. 60, 655 (1988); (Foundations)


 * L. Bombelli, J. Lee, D. Meyer, R.D. Sorkin, 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, Space-time code, Phys. Rev. 184:1261 (1969); (Foundations)


 * D. Finkelstein, "Superconducting" Causal Nets, Int. J. Th. Phys 27:473(1988);  (Foundations)


 * G. Hemion, A quantum theory of space and time; Found. Phys. 10 (1980), p. 819 (Similar proposal)


 * J. Myrheim, 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, 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, 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); gr-qc/9706002; (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, 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.); gr-qc/9511063; (Philosophical, Historical)


 * E.C. Zeeman, 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); gr-qc/9909075; (General);


 * R.D. Sorkin; Causal set glossary and bibliography (20 November 2001); (Glossary and bibliography);


 * R.D. Sorkin 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; 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); gr-qc/0002053 (Closeness of Lorentzian manifolds, Manifoldness)


 * A.R. Daughton, 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; gr-qc/0601069; (Continuum limit, Sprinkling)


 * S. Major, D.P. Rideout, S. Surya, On Recovering Continuum Topology from a Causal Set, J.Math.Phys.48:032501,2007; gr-qc/0604124 (Continuum Topology)


 * S. Major, D.P. Rideout, S. Surya, Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory, 0902.0434 (Continuum topology and homology)


 * D.A. Meyer, 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, Spherical containment and the Minkowski dimension of partial orders, Order 10: 227-237 (1993); (Dimension theory)


 * J. Noldus, 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, 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; gr-qc/0207103v2 (Dimension theory)


 * R.D. Sorkin; 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; 0712.1648


 * S. Surya, Recovering spacetime topology from a causet; Talk given at Loops 05, 10-14 October 2005, Potsdam, Max Planck Institute for Gravitational Physics (Topology)

Cosmological Constant

 * M. Ahmed, S. Dodelson, P.B. Greene, R.D. Sorkin, Everpresent lambda;  Phys. Rev. D69, 103523, (2004) astro-ph/0209274v1 ;   (Cosmological Constant)


 * Y. Jack Ng and H. van Dam, A small but nonzero cosmological constant; Int. J. Mod. Phys D. 10 : 49 (2001) hep-th/9911102v3; (PreObservation Cosmological Constant)


 * Y. Kuznetsov, On cosmological constant in Causal Set theory; 0706.0041


 * 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; 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, 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) gr-qc/9706002 ; (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; gr-qc/0503057v1; (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; 0710.1675; (Cosmological Constant)

Lorentz and Poincaré Invariance, Phenomenology

 * L. Bombelli, J. Henson, R.D. Sorkin; Discreteness without symmetry breaking: a theorem;  gr-qc/0605006v1; (Lorentz invariance, Sprinkling)


 * F. Dowker, J. Henson, R.D. Sorkin, Quantum gravity phenomenology, Lorentz invariance and discreteness; Mod. Phys. Lett. A19, 1829–1840, (2004) gr-qc/0311055v3; (Lorentz invariance, Phenomenology, Swerves)


 * F. Dowker, Causal Set Phenomenology; Talk given at Loops 05, 10-14 October 2005, Potsdam, Max Planck Institute for Gravitational Physics (Swerves)


 * J. Henson, Macroscopic observables and Lorentz violation in discrete quantum gravity; gr-qc/0604040v1; (Lorentz invariance, Phenomenology)


 * N. Kaloper, D. Mattingly, Low energy bounds on Poincaré violation in causal set theory; Phys. Rev. D 74, 106001 (2006) astro-ph/0607485 (Poincaré invariance, Phenomenology)


 * D. Mattingly, Causal sets and conservation laws in tests of Lorentz symmetry; Phys. Rev. D 77, 125021 (2008) 0709.0539 (Lorentz invariance, Phenomenology)


 * L. Philpott, F. Dowker, R.D. Sorkin, Energy-momentum diffusion from spacetime discreteness; 0810.5591 (Phenomenology, Swerves)


 * J. Scargle, 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, 0711.2904

Black Hole Entropy

 * D. Dou, Causal Sets, a Possible Interpretation for the Black Hole Entropy, and Related Topics; PhD thesis (SISSA, Trieste, 1999); gr-qc/0106024 (Black hole entropy)


 * D. Dou, Black Hole Entropy as Causal Links; Fnd. of Phys, 33 2:279-296(18) (2003); gr-qc/0302009v1  (Black hole entropy)


 * G.'t Hooft, 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 ; gr-qc/0612074v1; (Black hole entropy)


 * D.P. Rideout, S. Zohren, Evidence for an entropy bound from fundamentally discrete gravity; Class.Quant.Grav. 23 (2006) 6195-6213; gr-qc/0606065v2 (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, 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;gr-qc/0403085v2 (Quantum Measure Theory)


 * R.B. Salgado; Some Identities for the Quantum Measure and its Generalizations; gr-qc/9903015; (Quantum Measure Theory)


 * R.D. Sorkin; Quantum mechanics as quantum measure theory; Mod.Phys.Lett.A9:3119-3128,1994; gr-qc/9401003v2  (Quantum Measure Theory)


 * R.D. Sorkin; Quantum measure theory and its interpretation; 4TH Drexel Symposium on Quantum Nonintegrability, 8-11 Sep 1994, Philadelphia, PA; gr-qc/9507057; (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 hep-th/0310166 (Quantum field theory)


 * G. Hemion, A discrete geometry: speculations on a new framework for classical electrodynamics; Int. J. Theor. Phys. 27 (1988), p. 1145 (Classical electodynamics)


 * S. Johnston; 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; 0806.3083 (Quantum Field Theory)


 * R.D. Sorkin; Does Locality Fail at Intermediate Length-Scales; Towards Quantum Gravity, Daniele Oriti (ed.) (Cambridge University Press, 2007); gr-qc/0703099v1; (d'Alembertian, Locality)


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


 * R. Sverdlov; 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; 0801.0240


 * R. Sverdlov; A Geometrical Description of Spinor Fields; 0802.1914


 * R. Sverdlov; Bosonic Fields in Causal Set Theory; 0807.4709


 * R. Sverdlov; Gauge Fields in Causal Set Theory; 0807.2066


 * R. Sverdlov; Spinor fields in Causal Set Theory; 0808.2956


 * R. Sverdlov; Quantum Field Theory and Gravity in Causal Sets; PhD Thesis (University of Michigan 2009); 0905.2263 (Quantum Field Theory and Gravity)

Dynamics

 * A.Ash, P. McDonald, Moment Problems and the Causal Set Approach to Quantum Gravity; J.Math.Phys. 44 (2003) 1666-1678; gr-qc/0209020


 * A.Ash, P. McDonald, Random partial orders, posts, and the causal set approach to discrete quantum gravity; J.Math.Phys. 46 (2005) 062502 (Analysis of number of posts in growth processes)


 * 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).;gr-qc/0202097; (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); gr-qc/0210061; (Cosmology, Dynamics, Observables)


 * G. Brightwell, J. Henson, S. Surya; A 2D model of Causal Set Quantum Gravity: The emergence of the continuum; 0706.0375; (Quantum Dynamics, Toy Model)


 * G.Brightwell, N. Georgiou; 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); gr-qc/9811088; (Quantum Dynamics, Toy Model)


 * F. Dowker, S. Surya; Observables in extended percolation models of causal set cosmology;Class. Quant. Grav. 23, 1381-1390 (2006); gr-qc/0504069v1; (Cosmology, Dynamics, Observables)


 * M. Droste, Universal homogeneous causal sets, J. Math. Phys. 46, 122503 (2005); gr-qc/0510118; (Past-finite causal sets)


 * J. Henson; Comparing causality principles; Stud.Hist.Philos.Mod.Phys. 36 (2005) 519-543; quant-ph/0410051v3; (Quantum Dynamics, Philosophy)


 * A.L. Krugly; 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; gr-qc/0506133v2; (Observables, Continuum topology)


 * A. Mallios, I. Raptis; Finitary Spacetime Sheaves of Quantum Causal Sets: Curving Quantum Causality gr-qc/0102097


 * F. Markopoulou; The internal description of a causal set: What the universe looks like from the inside Commun.Math.Phys. 211 (2000) 559-583 gr-qc/9811053


 * 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); gr-qc/0009063 (Cosmology, Dynamics)


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


 * D.A. Meyer; 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: 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, gr-qc/0201004v8


 * I. Raptis; Algebraic Quantization of Causal Sets; Int.J.Theor.Phys 39:1233-1240,2000; gr-qc/9906103; (Algebraic quantization);


 * D.P. Rideout, R.D. Sorkin; A classical sequential growth dynamics for causal sets, Phys. Rev D, 6, 024002 (2000);gr-qc/9904062 (Cosmology, Dynamics)


 * D.P. Rideout, R.D. Sorkin; Evidence for a continuum limit in causal set dynamics Phys.Rev.D63:104011,2001; gr-qc/0003117(Cosmology, Dynamics)


 * D.P. Rideout; Dynamics of Causal Sets; PhD Thesis (Syracuse University 2001); gr-qc/0212064; (Cosmology, Dynamics)


 * D.P. Rideout; Spatial Hypersurfaces in Causal Set Cosmology; Talk given at Loops 05, 10-14 October 2005, Potsdam, Max Planck Institute for Gravitational Physics (Spatial hyper-surfaces, Dynamics)


 * R.D. Sorkin; Indications of causal set cosmology; Int. J. Theor. Ph. 39(7):1731-1736 (2000); gr-qc/0003043; (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); gr-qc/0703098v1; (Dynamics, Philosophy)


 * R.D. Sorkin; Two Talks given at the 1997 Santa Fe workshop: A Review of the Causal Set Approach to Quantum Gravity and 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; gr-qc/0504066v3; (Cosmology, Dynamics)

Geometry

 * E. Bachmat; Discrete spacetime and its applications; gr-qc/0702140; (Geodesics, Antichains)


 * G. Brightwell, R. Gregory; 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 hep-th/0703098 (Causal intervals)


 * S.W. Hawking, A.R. King, P.J. McCarthy; 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)


 * S. He, D.P. Rideout; A Causal Set Black Hole; 0811.4235 (Causal structure of Schwarzschild spacetime, Sprinklings)


 * R. Ilie, G.B. Thompson, D.D. Reid; A numerical study of the correspondence between paths in a causal set and geodesics in the continuum; 2006 Class. Quantum Grav. 23 3275-3285 gr-qc/0512073(Geodesic length)


 * 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; The class of continuous timelike curves determines the topology of spacetime; J. Math. Phys. 18 7:1399-1404 (1977); (Geometry, Causal Structure)


 * D.P. Rideout, P. Wallden; Spacelike distance from discrete causal order; 0810.1768 (Spatial distances)


 * A.A. Robb ; A theory of time and space; Cambridge University Press, 1914; (Geometry, Causal Structure)


 * A.A. Robb ; The absolute relations of time and space; Cambridge University Press, 1921; (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); gr-qc/9508018 (Causal Structure)

Order Theory

 * N. Alon, B. Bollobas, G. Brightwell, S. Janson; Linear extensions of a random partial order; Ann. Applied Prob. 4: 108-123 (1994); (Random partial orders);


 * B. Bollobas, G. Brightwell; Box spaces and random partial orders; Trans. Amer. Math. Soc 324(1): 59-72 (1991); (Random partial orders);


 * B. Bollobas, G. Brightwell; The Height of a Random Partial Order: Concentration of Measure; Annals of Applied Probability 2: 1009-1018 (1992); (Geodesics);


 * B. Bollobas, G. Brightwell; 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; M. Luczak; Order-invariant Measures on Causal Sets; 0901.0240; (Measures on causal sets)


 * G. Brightwell; M. Luczak; Order-invariant Measures on Fixed Causal Sets; 0901.0242; (Measures on causal sets)


 * G. Brightwell, P. Winkler; Sphere Orders; Order 6:235-240 (1989); (Order Theory);


 * D. Crippa, K. Simon, P. Trunz; Markov Processes Involving q-Stirling Numbers; Combinatorics, Probability and Computing 6: 165-178 (1997);;;


 * D. Dhar; 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; 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; Finite three dimensional partial orders which are not sphere orders; Discrete Math. 201: 101-132 (1999);;


 * N. Georgiou; A Random Binary Order: A New Model of Random Partial Orders; CDAM Research Report, LSE-CDAM-2003-17


 * J.H. Kim, B. Pittel; On tail distribution of interpost distance; J. Combinatorial Theory, B 80 1:49-56 (2000); (Geodesics);


 * D.J. Kleitman, B.L. Rothschild; The Number of Finite Topologies; Proc. Amer. Math. Society 25:276-282 (1970); (Order Theory);


 * D.J. Kleitman, B.L. Rothschild; 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; A Phase Transition on Partial Orders; Physica 96A:254-259 (1979);; (Phase Transitions for Posets, Order Theory);


 * C. M. Newman; Chain Lengths in Certain Random Directed Graphs; Random Structures and Algorithms 3: 243-253 (1992); ; (Chain lengths);


 * B. Pittel, R. Tungol; 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; 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; 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;math/0309126v1; (Order theory);