## Publications

The preprints are also available at preprint servers arxiv.org

**Books and proceedings:**

**Combinatorics and Random Matrix Theory**(with P. Deift and T. Suidan), 461 pages, American Mathematical Society, 2016**Handbook of Random Matrix Theory**(with G. Akemann and P. Di Francesco), 960 pages, Oxford University Press, 2011**Discrete orthogonal polynomials. Asymptotics and applications**(with T.Kriecherbauer, K.McLaughlin and P.Miller) Annals of Math Studies, 164. Princeton University Press, Princeton, NJ 2007.**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.

**Papers:**

**Pinched-up periodic KPZ fixed point**(with Z. Liu) 03/02/2024,42 pp. PDF, 2024.**Differential equations for the KPZ and periodic KPZ fixed points**(with A. Prokhorov and G. Silva) 08/24/2022,45 pp. PDF, Comm. Math. Phys., 401, 1753--1806, 2023.**KPZ limit theorems**09/01/2021, 19 pp. (a survey paper for ICM 2022 proceedings) PDF,**Spherical spin glass model with external field**(with E. Collins-Woodfin, P. Le Doussal, and H. Wu) 10/11/2020, 04/04/2021, 75 pp. PDF, J. Stat. Phys. 183(2), 2021**Limiting one-point distribution of periodic TASEP**(with Z. Liu and G. Silva) 08/16/2020, 64 pp. PDF, Annales de l’Institut Henri Poincaré 58(1), 248--302, 2022**Edge distribution of thinned real eigenvalues in the real Ginibre ensemble**(with Thomas Bothner) 08/04/2020, 36 pp. PDF, Ann. Henri Poincaré 23(11), 4003--4056, 2022**Periodic TASEP with general initial conditions**(with Z. Liu) 12/20/2019, 09/12/2020 (revision) 77 pp. PDF, Prob. Theory Related Fields 179(3-4), 1047–1144, 2021**The largest real eignvalue in the real Ginibre ensemble and its relation to the Zakharov-Shabat system**(with Thomas Bothner) 08/07/2018, 06/12/2020 (revision) 34 pp. PDF, Annals of Appl. Prob. 30(1), 460--501, 2020.**Ferromagnetic to paramagnetic transition in spherical spin glass**(with Ji Oon Lee and Hao Wu) 5/15/2018 41 pp. PDF, J. Stat. Phys. 173(5), 1484--1522, 2018**Free energy of bipartite spherical Sherrington-Kirkpatrick model**(with Ji Oon Lee) 11/17/2017 43 pp. PDF, Ann. Inst. Henri Poincaré Probab. Stat. 56(4), 2897--2934, 2020**Multi-point distribution of periodic TASEP**(with Z. Liu) 10/09/2017, 10/26/2018 (revision) 59 pp. PDF, J. Amer. Math. Soc. 32(3), 609--674, 2019.**Facilitated exclusion process**(with G. Barraquand, I. Cowrin, T. Suidan) 07/06/2017 (revision) 26 pp. PDF, Computation and combinatorics in dynamics, stochastics and control, 1-35, Abel Symposium 13, Springer, Cham, 2018.**TASEP on a ring in sub-relaxation time scale**(with Z. Liu) 09/02/2016, 10/27/2016 (revision) 32 pp. PDF J. Stat. Phys. 165(6), 1051-1085, 2016**Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with ferromagnetic interaction**(with Ji Oon Lee) 07/05/2016, 07/14/2016 (revision) 32 pp. PDF Annales Henri Poincaré 18(6), 1867-1917, 2017.**Pfaffian Schur processes and last passage percolation in a half-quadrant**(with G. Barraquand, I. Cowrin, T. Suidan) 06/01/2016, 07/06/2017 (revision) 57 pp. PDF Annals of Probability 46(6), 3015-3089, 2018.**Fluctuations of TASEP on a ring in relaxation time scale**(with Z. Liu) 05/24/2016, 02/06/2017 (revision) 51 pp. PDF Comm. Pure Appl. Math. 71(4), 747--813, 2018.**Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model**(with Ji Oon Lee) 06/15/2015, 08/02/2016 (revision), 41 pp. PDF J. Stat. Phys. 165(2), 185-224, 2016**On the average of the Airy process and its time reversal**(with Z. Liu) 08/05/2013, 11/20/2013 (revision), 12 pp. PDF Electron. Commun. Probab.18, no.89, 10pp. 2013**Circular unitary ensemble with highly oscillatory potential**06/01/2013, 13 pp. PDF (not to be published anywhere)**Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes**(with Z. Liu) 12/18/2012, 5/16/2013 (revision) 30 pp. PDF Int. Math. Res. Not.**Convergence of the two-point function of the stationary TASEP**(with P. Ferrari and S. Peche) 8/31/2012, 18 pp. PDF*Singular phenomena and scaling in mathematical models,*91–110,*Springer, Cham,*2014.**On a relationship between high rank cases and rank one cases of Hermitian random matrix models with external source**(with D. Wang) 7/2/2012, 10/21/2012, 17 pp. PDF*Random matrix theory, interacting particle systems, and integrable systems,*25–38, MSRI Publ., 65,*Cambridge Univ. Press, New York,*2014.**Batch latency analysis and phase transitions for a tandem of queues with exponentially distributed service times**(with R. R. Nadakuditi) 6/14/2012, 3/10/2014 (revision) 26 pp. PDF Queueing Systems 78(3), 255--285, 2014 .**On the joint distribution of the maximum and its position of the Airy2 process minus a parabola**(with K. Liechty and G. Schehr) 5/16/2012, 15 pp. PDF J. Math. Phys. 53(8):083303, 2012.**Universality for directed polymers in thin rectangles**(with A. Auffinger and I. Corwin) 4/19/2012, 12 pp. PDF (not to be published anywhere)**Limiting distribution of maximal crossing and nesting of Poissonized random matchings**(with R. Jenkins) 9/11/2011, 49 pp. PDF Annals of Probability 41(6):4359-4406, 2013**On the largest eigenvalue of a Hermitian random matrix model with spiked external source II. Higher rank cases**(with D. Wang) 4/14/2011, 5/29/2012 (revision) 57 pp. PDF Int. Math. Res. Not.issue 14:3304--3370, 2013**On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case**(with D. Wang) 10/21/2010, 12/18/2010, 61 pp. PDFInt. Math. Res. Not.issue 22:5164--5240, 2011**Limit process of stationary TASEP near the characteristic line**(with P. Ferrari and S. Peche) 07/01/2009, 59 pp. PDF Comm. Pure Appl. Math., 63(8): 1017--1070, 2010.**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**On the Christoffel-Darboux kernel for random Hermitian matrices with external source**09/23/2008, 16 pp. PDF CMFT. 9(1):455--471, 2009.**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.**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.**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.**Painleve formulas of the limiting distributions for non-null complex sample covariance matrices**PDF. 04/22/05, 24 pp. revised 07/20/50, 25 pp. Duke Math. J., 133(2):205--235, 2006. Correction**A GUE Central Limit Theorem and Universality of Directed Last and First Passage Site Percolation**(with T. M. Suidan) PDF. 12/14/04, 8 pp. Int. Math. Res. Not., no.6:325--338, 2005.**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.**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**Limiting distribution of last passage percolation models**PDF. 07/21/03, 8 pp. a survey paper. XIVth International Congress on Mathematical Physics, 339--346, World Sci. Publ., Hackensack, NJ, 2005.**Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices**(with P.Deift and E.Strahov) PDF. 04/9/03, 18 pp. J. Math. Phys., 44 (8):3657-3670, 2003**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. 01/07/03, 29 pp. Int. Math. Res. Not., no.15:821-858, 2003 (Full version of this paper appeared as a book.)**Painleve expressions for LOE, LSE and interpolating ensembles**PDF. 05/06/02, 41 pp., 2 figures. Int. Math. Res. Not., no.33:1739-1789, 2002**Optimal tail estimates for directed last passage site percolation with geometric random variables**(with Percy Deift, Ken McLaughlin, Peter Miller and Xin Zhou) PDF. 12/18/01, 41 pp. Adv. Theor. Math. Phys., 5, no.6:1207-1250, 2001**Riemann-Hilbert problems for last passage percolation**PDF. 07/01/01, 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.**A Fredholm determinant identy and the convergence of moments for random Young tableaux**(with P.Deift and E.Rains) PDF. 12/14/00, rev.1/1/01, 45 pp. Comm. Math. Phys., 223, no.3:627-672, 2001**Limiting distributions for a polynuclear growth model with external sources**(with E.Rains) PDF. 03/22/00, 15pp. J. Stat. Phys., 100, issue 3/4:523-541, Aug. 2000.**Random vicious walks and random matrices**PDF. 12/29/99, 2/26/00 (revised), 24pp. Comm. Pure Appl. Math, 53, no.11:1385-1410, Nov. 2000.**Symmetrized random permutations**(with E.Rains) PDF. survey of the paper (4) and related topics. 9/23/99, 17 pp. MSRI volume 40 : Random Matrix Models and Their Applications , 1-19, 2001, edited by P. Bleher and A. Its**The asymptotics of monotone subsequences of involutions**(with E. Rains) PDF. 05/12/99, 1/31/01 (revised), sequel to the paper below. 65 pp. Duke Math. J., 109, issue 2:205-281, 2001

**Algebraic aspects of increasing subsequences**(with E. Rains) PDF. 05/12/99, 9/9/99 (revised), 51 pp. Duke Math. J., 109, issue 1:1-65, 2001**On the distribution of the length of the second row of a Young diagram under Plancherel measure**(with P. Deift and K. Johansson) PDF. 01/15/99, 25pp. Geom. Funct. Anal., 10, no.4:702-731, 2000**On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations**(with P. Deift and K. Johansson) PDF. 07/02/98, 60pp. J. Amer. Math. Soc., 12, no.4:1119-1178, 1999