Research

Limit theorems in combinatorics: longest increasing subsequence of random permutation, Plancherel measure on partitions, symmetrized random permutaitons, maximal crossing and nesting of random matching

Random matrix theory: discrete orthogonal polynomial ensembles, spiked sample covariance matrices, Hermitian matrix model with external source, universality of random matrix theory

Applications to Statistics: transitional behavior of spiked sample covariance matrices, tandem queues

Universality: discrete orthogonal polynomial ensemble, last passage percolation, non-intersecting walks, Hermitian matrix model with spiked external source

Tracy-Widom distribution and Painleve: properties of TW distributions, total integrals of Painleve II, Riemann-Hilbert problem

Last passage percolation, random growth, interacting particle systems: PNG model, TASEP, phase transition, limit theorems, limit process

Non-intersecting processes: random vicious walks, random tiling of hexagon, bus system in Cuernevaca

 

Spin glass: spherical Sherrington-Kirkpatrik model

Coauthors: Guillaume Barraquand, Gerard Ben Arous,  Alexei Borodin,  Robbie Buckingham,  Ivan Corwin, Percy Deift,  Jeff DiFranco,  Patrik Ferrari,  Alexander Its,  Bob Jenkins,  Kurt Johansson, Thomas Kriecherbauer,  Ji Oon Lee, Karl Liechty,  Zhipeng Liu, Ken T.-R. McLaughlin,  Peter Miller, Raj Rao Nadakuditi,  Sandrine Peche,  Eric Rains,  Gregory Schehr,  Jack Silverstein, Eugene Strahov,  Toufic Suidan,  Dong Wang,  Xin Zhou