Determinantal probability measures

 Access to full text

 Full (PDF)

1. 1. D. J. Aldous (1990), The random walk construction of uniform spanning trees and uniform labelled trees. SIAM J. Discrete Math., 3, 450–465. Zbl0717.05028MR1069105
2. 2. N. Alon and J. H. Spencer (2001), The Probabilistic Method. Second edition. New York: John Wiley & Sons Inc. Zbl0767.05001MR1885388
3. 3. I. Benjamini, R. Lyons, Y. Peres, and O. Schramm (1999), Group-invariant percolation on graphs. Geom. Funct. Anal., 9, 29–66. Zbl0924.43002MR1675890
4. 4. I. Benjamini, R. Lyons, Y. Peres, and O. Schramm (2001), Uniform spanning forests. Ann. Probab., 29, 1–65. Zbl1016.60009MR1825141
5. 5. J. van den Berg, and H. Kesten (1985), Inequalities with applications to percolation and reliability. J. Appl. Probab., 22, 556–569. Zbl0571.60019MR799280
6. 6. A. Beurling and P. Malliavin (1967), On the closure of characters and the zeros of entire functions. Acta Math., 118, 79–93. Zbl0171.11901MR209758
7. 7. A. Borodin (2000), Characters of symmetric groups, and correlation functions of point processes. Funkts. Anal. Prilozh., 34, 12–28, 96. English translation: Funct. Anal. Appl., 34(1), 10–23. Zbl0959.60037MR1747821
8. 8. A. Borodin, A. Okounkov, and G. Olshanski (2000), Asymptotics of Plancherel measures for symmetric groups. J. Am. Math. Soc., 13, 481–515 (electronic). Zbl0938.05061MR1758751
9. 9. A. Borodin and G. Olshanski (2000), Distributions on partitions, point processes, and the hypergeometric kernel. Comment. Math. Phys., 211, 335–358. Zbl0966.60049MR1754518
10. 10. A. Borodin and G. Olshanski (2001), z-measures on partitions, Robinson-Schensted-Knuth correspondence, and β=2 random matrix ensembles. In P. Bleher and A. Its, eds., Random Matrix Models and Their Applications, vol. 40 of Math. Sci. Res. Inst. Publ., pp. 71–94. Cambridge: Cambridge Univ. Press. Zbl0987.15013
11. 11. A. Borodin and G. Olshanski (2002), Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. Preprint. Zbl1082.43003MR2180403
12. 12. J. Bourgain and L. Tzafriri (1987), Invertibility of “large” submatrices with applications to the geometry of Banach spaces and harmonic analysis. Isr. J. Math., 57, 137–224. Zbl0631.46017
13. 13. A. Broder (1989), Generating random spanning trees. In 30th Annual Symposium on Foundations of Computer Science (Research Triangle Park, North Carolina), pp. 442–447. New York: IEEE. 
14. 14. R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte (1940), The dissection of rectangles into squares. Duke Math. J., 7, 312–340. Zbl0024.16501MR3040
15. 15. R. M. Burton and R. Pemantle (1993), Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances. Ann. Probab., 21, 1329–1371. Zbl0785.60007MR1235419
16. 16. J. Cheeger and M. Gromov (1986), L2-cohomology and group cohomology. Topology, 25, 189–215. Zbl0597.57020MR837621
17. 17. Y. B. Choe, J. Oxley, A. Sokal, and D. Wagner (2003), Homogeneous multivariate polynomials with the half-plane property. Adv. Appl. Math. To appear. Zbl1054.05024MR2037144
18. 18. J. B. Conrey (2003), The Riemann hypothesis. Notices Am. Math. Soc., 50, 341–353. Zbl1160.11341MR1954010
19. 19. J. B. Conway (1990), A Course in Functional Analysis. Second edition. New York: Springer. Zbl0706.46003MR1070713
20. 20. J. P. Conze (1972/73), Entropie d’un groupe abélien de transformations. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 25, 11–30. Zbl0261.28015
21. 21. D. J. Daley and D. Vere-Jones (1988), An Introduction to the Theory of Point Processes. New York: Springer. Zbl0657.60069MR950166
22. 22. P. Diaconis (2003), Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture. Bull. Am. Math. Soc., New Ser., 40, 155–178 (electronic). Zbl1161.15302MR1962294
23. 23. D. Dubhashi and D. Ranjan (1998), Balls and bins: a study in negative dependence. Random Struct. Algorithms, 13, 99–124. Zbl0964.60503MR1642566
24. 24. F. J. Dyson (1962), Statistical theory of the energy levels of complex systems. III. J. Math. Phys., 3, 166–175. Zbl0105.41604MR143558
25. 25. T. Feder and M. Mihail (1992), Balanced matroids. In Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 26–38, New York. Association for Computing Machinery (ACM). Held in Victoria, BC, Canada. 
26. 26. R. M. Foster (1948), The average impedance of an electrical network. In Reissner Anniversary Volume, Contributions to Applied Mechanics, pp. 333–340. J. W. Edwards, Ann Arbor, Michigan. Edited by the Staff of the Department of Aeronautical Engineering and Applied Mechanics of the Polytechnic Institute of Brooklyn. Zbl0040.41801MR29773
27. 27. W. Fulton and J. Harris (1991), Representation Theory: A First Course. Readings in Mathematics. New York: Springer. Zbl0744.22001MR1153249
28. 28. D. Gaboriau (2002), Invariants l2 de relations d’équivalence et de groupes. Publ. Math., Inst. Hautes Étud. Sci., 95, 93–150. Zbl1022.37002
29. 29. H. O. Georgii (1988), Gibbs Measures and Phase Transitions. Berlin-New York: Walter de Gruyter & Co. Zbl0657.60122MR956646
30. 30. O. Häggström (1995), Random-cluster measures and uniform spanning trees. Stochastic Processes Appl., 59, 267–275. Zbl0840.60089MR1357655
31. 31. P. R. Halmos (1982), A Hilbert Space Problem Book. Second edition. Encycl. Math. Appl. 17, New York: Springer. Zbl0496.47001MR675952
32. 32. D. Heicklen and R. Lyons (2003), Change intolerance in spanning forests. J. Theor. Probab., 16, 47–58. Zbl1019.60092MR1956820
33. 33. K. Johansson (2001), Discrete orthogonal polynomial ensembles and the Plancherel measure. Ann. Math. (2), 153, 259–296. Zbl0984.15020MR1826414
34. 34. K. Johansson (2002), Non-intersecting paths, random tilings and random matrices. Probab. Theory Relat. Fields, 123, 225–280. Zbl1008.60019MR1900323
35. 35. G. Kalai (1983), Enumeration of Q-acyclic simplicial complexes. Isr. J. Math., 45, 337–351. Zbl0535.57011MR720308
36. 36. Y. Katznelson and B. Weiss (1972), Commuting measure-preserving transformations. Isr. J. Math., 12, 161–173. Zbl0239.28014MR316680
37. 37. G. Kirchhoff (1847), Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird. Ann. Phys. Chem., 72, 497–508. 
38. 38. R. Lyons (1998), A bird’s-eye view of uniform spanning trees and forests. In D. Aldous and J. Propp, eds., Microsurveys in Discrete Probability, vol. 41 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 135–162. Providence, RI: Am. Math. Soc., Papers from the workshop held as part of the Dimacs Special Year on Discrete Probability in Princeton, NJ, June 2–6, 1997. Zbl0909.60016
39. 39. R. Lyons (2000), Phase transitions on nonamenable graphs. J. Math. Phys., 41, 1099–1126. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. Zbl1034.82014MR1757952
40. 40. R. Lyons (2003), Random complexes and ℓ2-Betti numbers. In preparation. 
41. 41. R. Lyons, Y. Peres, and O. Schramm (2003), Minimal spanning forests. In preparation. Zbl1142.60065
42. 42. R. Lyons and J. E. Steif (2003), Stationary determinantal processes: Phase multiplicity, Bernoullicity, entropy, and domination. Duke Math. J. To appear. Zbl1068.82010MR2030095
43. 43. O. Macchi (1975), The coincidence approach to stochastic point processes. Adv. Appl. Probab., 7, 83–122. Zbl0366.60081MR380979
44. 44. S. B. Maurer (1976), Matrix generalizations of some theorems on trees, cycles and cocycles in graphs. SIAM J. Appl. Math., 30, 143–148. Zbl0364.05021MR392635
45. 45. M. L. Mehta (1991), Random Matrices. Second edition. Boston, MA: Academic Press Inc. Zbl0780.60014MR1083764
46. 46. B. Morris (2003), The components of the wired spanning forest are recurrent. Probab. Theory Related Fields, 125, 259–265. Zbl1031.60035MR1961344
47. 47. C. M. Newman (1984), Asymptotic independence and limit theorems for positively and negatively dependent random variables. In Y. L. Tong, ed., Inequalities in Statistics and Probability, pp. 127–140. Hayward, CA: Inst. Math. Statist. Proceedings of the symposium held at the University of Nebraska, Lincoln, Neb., October 27–30, 1982. MR789244
48. 48. A. Okounkov (2001), Infinite wedge and random partitions. Sel. Math., New Ser., 7, 57–81. Zbl0986.05102MR1856553
49. 49. A. Okounkov and N. Reshetikhin (2003), Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram. J. Am. Math. Soc., 16, 581–603 (electronic). Zbl1009.05134MR1969205
50. 50. D. S. Ornstein and B. Weiss (1987), Entropy and isomorphism theorems for actions of amenable groups. J. Anal. Math., 48, 1–141. Zbl0637.28015MR910005
51. 51. J. G. Oxley (1992), Matroid Theory. New York: Oxford University Press. Zbl1115.05001MR1207587
52. 52. R. Pemantle (1991), Choosing a spanning tree for the integer lattice uniformly. Ann. Probab., 19, 1559–1574. Zbl0758.60010MR1127715
53. 53. R. Pemantle (2000), Towards a theory of negative dependence. J. Math. Phys., 41, 1371–1390. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. Zbl1052.62518MR1757964
54. 54. J. G. Propp and D. B. Wilson (1998), How to get a perfectly random sample from a generic Markov chain and generate a random spanning tree of a directed graph. J. Algorithms, 27, 170–217. 7th Annual ACM-SIAM Symposium on Discrete Algorithms (Atlanta, GA, 1996). Zbl0919.68092MR1622393
55. 55. R. Redheffer (1972), Two consequences of the Beurling-Malliavin theory. Proc. Am. Math. Soc., 36, 116–122. Zbl0266.42017MR322439
56. 56. R. M. Redheffer (1977), Completeness of sets of complex exponentials. Adv. Math., 24, 1–62. Zbl0358.42007MR447542
57. 57. K. Seip and A. M. Ulanovskii (1997), The Beurling-Malliavin density of a random sequence. Proc. Am. Math. Soc., 125, 1745–1749. Zbl0914.42005MR1371141
58. 58. Q. M. Shao (2000), A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theor. Probab., 13, 343–356. Zbl0971.60015MR1777538
59. 59. Q. M. Shao and C. Su (1999), The law of the iterated logarithm for negatively associated random variables. Stochastic Processes Appl., 83, 139–148. Zbl0997.60023MR1705604
60. 60. T. Shirai and Y. Takahashi (2000), Fermion process and Fredholm determinant. In H. G. W. Begehr, R. P. Gilbert, and J. Kajiwara, eds., Proceedings of the Second ISAAC Congress, vol. 1, pp. 15–23. Kluwer Academic Publ. International Society for Analysis, Applications and Computation, vol. 7. Zbl1036.60045MR1940779
61. 61. T. Shirai and Y. Takahashi (2002), Random point fields associated with certain Fredholm determinants I: fermion, Poisson and boson point processes. Preprint. Zbl1051.60052MR2018415
62. 62. T. Shirai and Y. Takahashi (2003), Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic and Gibbs properties. Ann. Probab., 31, 1533–1564. Zbl1051.60053MR1989442
63. 63. T. Shirai and H. J. Yoo (2002), Glauber dynamics for fermion point processes. Nagoya Math. J., 168, 139–166. Zbl1029.82025MR1942400
64. 64. A. Soshnikov (2000a), Determinantal random point fields. Usp. Mat. Nauk, 55, 107–160. Zbl0991.60038MR1799012
65. 65. A. B. Soshnikov (2000b), Gaussian fluctuation for the number of particles in Airy, Bessel, sine, and other determinantal random point fields. J. Stat. Phys., 100, 491–522. Zbl1041.82001MR1788476
66. 66. V. Strassen (1965), The existence of probability measures with given marginals. Ann. Math. Stat., 36, 423–439. Zbl0135.18701MR177430
67. 67. C. Thomassen (1990), Resistances and currents in infinite electrical networks. J. Combin. Theory, Ser. B, 49, 87–102. Zbl0706.94029MR1056821
68. 68. J. P. Thouvenot (1972), Convergence en moyenne de l’information pour l’action de Z2. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 24, 135–137. Zbl0266.60037
69. 69. A. M. Vershik and S. V. Kerov (1981), Asymptotic theory of the characters of a symmetric group. Funkts. Anal. i Prilozh., 15, 15–27, 96. English translation: Funct. Anal. Appl., 15(4), 246–255 (1982). Zbl0507.20006MR639197
70. 70. D. J. A. Welsh (1976), Matroid Theory. London: Academic Press [Harcourt Brace Jovanovich Publishers]. L. M. S. Monographs, No. 8. Zbl0343.05002MR427112
71. 71. N. White, ed. (1987), Combinatorial Geometries. Cambridge: Cambridge University Press. Zbl0626.00007MR921064
72. 72. H. Whitney (1935), On the abstract properties of linear dependence. Am. J. Math., 57, 509–533. Zbl0012.00404MR1507091
73. 73. H. Whitney (1957), Geometric Integration Theory. Princeton, N.J.: Princeton University Press. Zbl0083.28204MR87148
74. 74. D. B. Wilson (1996), Generating random spanning trees more quickly than the cover time. In Proceedings of the Twenty-eighth Annual ACM Symposium on the Theory of Computing, pp. 296–303. New York: ACM. Held in Philadelphia, PA, May 22–24, 1996. Zbl0946.60070MR1427525
75. 75. L. X. Zhang (2001), Strassen’s law of the iterated logarithm for negatively associated random vectors. Stochastic Processes Appl., 95, 311–328. Zbl1059.60042
76. 76. L. X. Zhang and J. Wen (2001), A weak convergence for negatively associated fields. Stat. Probab. Lett., 53, 259–267. Zbl0994.60026MR1841627

1. Alexei Borodin, Loop-free Markov chains as determinantal point processes
2. Yannick Baraud, Estimation of the density of a determinantal process
3. Alexei Borodin, Maurice Duits, Limits of determinantal processes near a tacnode