Stochastic analysis and applications
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References
- Jinho Baik, Percy Deift, and Kurt Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999), no. 4, 1119–1178. MR 1682248, DOI 10.1090/S0894-0347-99-00307-0 2 N. Cancrini and F. Martinelli, On the spectral gap of Kawasaki dynamics under a mixing condition revisited. Probabilistic techniques in equilibrium and nonequilibrium statistical physics, J. Math. Phys. 41 (2000), 1391–1423.
- P. Erdős and A. Rényi, On the evolution of random graphs, Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 (1960), 17–61 (English, with Russian summary). MR 125031
- C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model. I. Introduction and relation to other models, Physica 57 (1972), 536–564. MR 359655
- Geoffrey Grimmett, Percolation, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 321, Springer-Verlag, Berlin, 1999. MR 1707339, DOI 10.1007/978-3-662-03981-6
- Alice Guionnet and Boguslaw Zegarlinski, Decay to equilibrium in random spin systems on a lattice, Comm. Math. Phys. 181 (1996), no. 3, 703–732. MR 1414307, DOI 10.1007/BF02101294
- Alice Guionnet and Boguslaw Zegarlinski, Decay to equilibrium in random spin systems on a lattice. II, J. Statist. Phys. 86 (1997), no. 3-4, 899–904. MR 1438973, DOI 10.1007/BF02199123 8 E. Ising, Beitrag zur Theorie des Ferromagnitismus, Z. Phys. 31 (1926), 253–258.
- P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938 10 Leif Jensen, Large deviations of the asymmetric simple exclusion process, Ph.D. thesis, Courant Inst., New York Univ., New York, 2000.
- Kurt Johansson, Shape fluctuations and random matrices, Comm. Math. Phys. 209 (2000), no. 2, 437–476. MR 1737991, DOI 10.1007/s002200050027 12 A. N. Kolmogorov, Über die analyttischen Methoden in der Wahrscheinlichkeitsrechnung, Math. Ann. 104 (1931), 415–458. 13 —, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer-Verlag, Berlin, 1933.
- Shigeo Kusuoka and Daniel Stroock, Applications of the Malliavin calculus. I, Stochastic analysis (Katata/Kyoto, 1982) North-Holland Math. Library, vol. 32, North-Holland, Amsterdam, 1984, pp. 271–306. MR 780762, DOI 10.1016/S0924-6509(08)70397-0
- S. Kusuoka and D. Stroock, Applications of the Malliavin calculus. III, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), no. 2, 391–442. MR 914028
- Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley, New York-Chichester-Brisbane, 1978, pp. 195–263. MR 536013
- C. M. Newman and D. L. Stein, Equilibrium pure states and nonequilibrium chaos, J. Statist. Phys. 94 (1999), no. 3-4, 709–722. MR 1675370
- J. Quastel, F. Rezakhanlou, and S. R. S. Varadhan, Large deviations for the symmetric simple exclusion process in dimensions $d\geq 3$, Probab. Theory Related Fields 113 (1999), no. 1, 1–84. MR 1670733, DOI 10.1007/s004400050202
- D. Stroock and B. Zegarliński, On the ergodic properties of Glauber dynamics, J. Statist. Phys. 81 (1995), no. 5-6, 1007–1019. MR 1361304, DOI 10.1007/BF02179301
- Shigeo Kusuoka and Daniel Stroock, Applications of the Malliavin calculus. I, Stochastic analysis (Katata/Kyoto, 1982) North-Holland Math. Library, vol. 32, North-Holland, Amsterdam, 1984, pp. 271–306. MR 780762, DOI 10.1016/S0924-6509(08)70397-0
- Alain-Sol Sznitman, Brownian motion, obstacles and random media, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. MR 1717054, DOI 10.1007/978-3-662-11281-6
- Michel Talagrand, Huge random structures and mean field models for spin glasses, Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), 1998, pp. 507–536. MR 1648045
- Michel Talagrand, The Sherrington-Kirkpatrick model: a challenge for mathematicians, Probab. Theory Related Fields 110 (1998), no. 2, 109–176. MR 1609019, DOI 10.1007/s004400050147
- Craig A. Tracy and Harold Widom, Level spacing distributions and the Bessel kernel, Comm. Math. Phys. 161 (1994), no. 2, 289–309. MR 1266485, DOI 10.1007/BF02099779
- S. R. S. Varadhan, The complex story of simple exclusion, Itô’s stochastic calculus and probability theory, Springer, Tokyo, 1996, pp. 385–400. MR 1439538
- S. R. S. Varadhan, Large deviations for interacting particle systems, Perplexing problems in probability, Progr. Probab., vol. 44, Birkhäuser Boston, Boston, MA, 1999, pp. 373–383. MR 1703141 27 Norbert Wiener, Differential space, J. Math. and Phys. 2 (1923), 131–174.
- Horng-Tzer Yau, Scaling limit of particle systems, incompressible Navier-Stokes equation and Boltzmann equation, Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), 1998, pp. 193–202. MR 1648154
- Horng-Tzer Yau, Logarithmic Sobolev inequality for lattice gases with mixing conditions, Comm. Math. Phys. 181 (1996), no. 2, 367–408. MR 1414837, DOI 10.1007/BF02101009
Additional Information
- S. R. S. Varadhan
- Affiliation: Courant Institute, New York University, New York, New York 10012-1110
- MR Author ID: 177175
- Email: Varadhan@cims.nyu.edu
- Received by editor(s): September 7, 2001
- Received by editor(s) in revised form: February 21, 2002
- Published electronically: October 16, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 40 (2003), 89-97
- MSC (2000): Primary 60-02
- DOI: https://doi.org/10.1090/S0273-0979-02-00968-0
- MathSciNet review: 1943135