Publications

The preprints are also available at preprint servers arxiv.org

Books and proceedings:

  1. Combinatorics and Random Matrix Theory (with P. Deift and T. Suidan), 461 pages, American Mathematical Society, 2016
  2. Handbook of Random Matrix Theory (with G. Akemann and P. Di Francesco), 960 pages, Oxford University Press, 2011
  3. 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.
  4. 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:

  1. Pinched-up periodic KPZ fixed point (with Z. Liu) 03/02/2024,42 pp. PDF, 2024.
  2. 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.
  3. KPZ limit theorems 09/01/2021, 19 pp. (a survey paper for ICM 2022 proceedings) PDF,
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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.
  9. 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
  10. 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
  11. 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.
  12. 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.
  13. 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
  14. 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.
  15. 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.
  16. 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.
  17. 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
  18. 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
  19. Circular unitary ensemble with highly oscillatory potential  06/01/2013, 13 pp. PDF (not to be published anywhere)
  20. 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.
  21. 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.
  22. 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.
  23. 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 .
  24. 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.
  25. Universality for directed polymers in thin rectangles (with A. Auffinger and I.  Corwin) 4/19/2012, 12 pp. PDF (not to be published anywhere)
  26. 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
  27. 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
  28. 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
  29. 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.
  30. 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
  31. On the Christoffel-Darboux kernel for random Hermitian matrices with external source 09/23/2008, 16 pp. PDF CMFT. 9(1):455--471, 2009.
  32. 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.
  33. 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.
  34. 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.
  35. 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
  36. 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.
  37. 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.
  38. 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
  39. 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.
  40. 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
  41. 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.)
  42. 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
  43. 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
  44. 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.
  45. 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
  46. 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.
  47. 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.
  48. 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
  49. 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
  50. 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
  51. 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
  52. 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