Publications
Also available at preprint servers xxx.lanl.gov
or front.math.ucdavis.edu
Books and Proceedings:
(1) Discrete orthogonal polynomials. Asymptotics and applications (with T.Kriecherbauer, K.McLaughlin and P.Miller) pdf 10/17/03, 152 pp. Annals of Math Studies, 164. Princeton University Press, Princeton, NJ 2007. This book is the full version of the anouncement paper (12).
(2) Integrable Systems, Random Matrix Theory, and Applications: In Honor of Percy Deift (with T. Kriecherbauer, L.-C. Li, K. McLaughlin and C. Tomei), Contemporary Mathematics, 458, AMS, Providence, RI, 2008. This is the proceedings of the Conference held in NYU, 2006 in honor of Deift's 60th birthday.
Papaers:
(24)
Limit process of stationary TASEP near the characteristic line
(with P. Ferrari and S. Peche) 07/01/2009, 59 pp.
pdf.
(23) Total Integrals of global solutions to Painleve II (with R. Buckingham, J. DiFranco and A. Its) 10/15/2008, 39 pp. pdf. Nonlinearity, 22:1021--1061, 2009.
(22) On the Christoffel-Darboux kernel for random Hermitian matrices with external source 09/23/2008, 16 pp. pdf. CMFT., 9(1):455--471, 2009.
(21) Asymptotics of Tracy-Widom distributions and the total integral
of a Painleve II function (with R. Buckingham and J. DiFranco) 04/30/2007, 29 pp. pdf.
Comm. Math. Phys., 280(2):463--497, 2008.
(20)
Random Matrix Central Limit Theorems for Non-Intersecting Random Walks
(with T. Suidan)
04/09/2006, 21 pp.
pdf.
Annals of Probability,
35(5):1807--1834, 2007.
(19)
A Model for the Bus System in Cuernevaca (Mexico)
(with A. Borodin, P. Deift and T. Suidan)
10/17/2005, 9 pp.
pdf.
J. Phys. A,
39:8965--8975, 2006.
(18)
Painleve formulas of the limiting distributions
for non-null complex sample covariance matrices
pdf, This paper finds Painleve
formulas of the functions appeared in the paper (16) below.
04/22/05, 24 pp. revised 07/20/50, 25 pp.
Duke Math. J., 133(2):205--235, 2006.
(17)
A GUE Central Limit Theorem and Universality of Directed
Last and First Passage Site Percolation
(with T. M. Suidan)
pdf
ps
12/14/04, 8 pp.
Int. Math. Res. Not., no.6:325--338, 2005.
(16)
Eigenvalues of Large Sample Covariance Matrices of Spiked
Population Models
(with J. W. Silverstein)
pdf
07/27/04, 24 pp.
Journal of Multivariate Analysis, 97(6):1382--1408, 2006.
(15)
Phase transition of the largest eigenvalue for
non-null complex sample covariance matrices
(with G.Ben Arous and S.Peche)
pdf
02/23/04, 52 pp.
Annals of Probability, 33(5):1643-1697, 2005
(14)
Limiting distribution of last passage percolation models
pdf
ps
7/21/03, 8 pp.
a survey paper. XIVth International Congress on Mathematical Physics, 339--346, World Sci. Publ., Hackensack, NJ, 2005.
(13)
Products and Ratios of Characteristic Polynomials of Random Hermitian
Matrices
(with P.Deift and E.Strahov)
pdf
ps
4/9/03, 18 pp.
J. Math. Phys., 44 (8):3657-3670, 2003
(12)
Uniform Asymptotics for Polynomials Orthogonal
With Respect to a General Class of Discrete Weights and
Universality Results for Associated Ensembles: Announcement of
Results
(with T.Kriecherbauer, K.McLaughlin and P.Miller)
pdf
1/7/03, 29 pp.
Int. Math. Res. Not., no.15:821-858, 2003
(Full version of this paper is (15) above.)
(11) Painleve expressions for LOE, LSE and interpolating ensembles
ps
pdf
5/6/02, 41 pp., 2 figures.
Int. Math. Res. Not., no.33:1739-1789, 2002
(10) Optimal tail estimates for directed last passage site
percolation with geometric random variables
(with Percy Deift, Ken McLaughlin, Peter Miller and Xin Zhou)
ps
pdf
12/18/01, 41 pp.
Adv. Theor. Math. Phys., 5, no.6:1207-1250, 2001
(9) Riemann-Hilbert problems for last passage percolation
ps
pdf
7/1/01, 24 pp.
Recent Developments in
Integrable Systems and Riemann-Hilbert Problems,
Contemporary Mathematics 326,
1--21, 2003, edited by K.McLaughlin and X.Zhou
a survey paper about the use of RHP in the context of last passage percolation
problems and related topics like longest increasing subsequence, random growth
models and random vicious walks.
(8) A Fredholm determinant identy and the convergence of
moments for random Young tableaux (with P.Deift and E.Rains)
ps
pdf
12/14/00, rev.1/1/01, 45 pp.
Comm. Math. Phys., 223,
no.3:627-672, 2001
(7) Limiting distributions for a polynuclear growth model
with external sources (with E.Rains)
ps
pdf
3/22/00, 15pp.
J. Stat. Phys., 100,
issue 3/4:523-541, Aug. 2000
(6) Random vicious walks and random matrices
ps
pdf
12/29/99, 2/26/00 (revised), 24pp.
Comm. Pure Appl. Math, 53, no.11:1385-1410,
Nov. 2000
(4) The asymptotics of monotone subsequences of involutions
(with E. Rains)
ps
pdf
5/12/99, 1/31/01 (revised),
sequel to the paper (3). 65 pp.
Duke Math. J., 109, issue 2:205-281, 2001
(3) Algebraic aspects of increasing subsequences
(with E. Rains)
ps
pdf
5/12/99, 9/9/99 (revised), 51 pp.
Duke Math. J., 109, issue 1:1-65, 2001
(2) On the distribution of the length of the second row of
a Young diagram under Plancherel measure
(with P. Deift and K. Johansson)
ps
pdf
1/15/99, 25pp.
Geom. Funct. Anal., 10, no.4:702-731, 2000
(1) On the Distribution of the Length of the Longest Increasing
Subsequence of Random Permutations
(with P. Deift and K. Johansson)
ps
pdf
7/2/98, 60pp.
J. Amer. Math. Soc., 12, no.4:1119-1178, 1999