### About

My research interests are in analysis, probability and mathematical physics. I have been using analytic tools to study probabilistic models. Some specific models include the eigenvalues of large random matrices, heights of randomly growing interface (melting, wetting, burning), locations of vicious random walkers (random tiling), longest increasing subsequence of random permutations (maximization in random environment), and so on. These models are often solvable explicitly and exhibit remarkable universal behavior. Though the problems are probabilistic, they can be treated by using analytic tools such as complex analysis, asymptotic analysis, functional analysis, potential theory, and combinatorics. I am also interested in integrable differential equations and various applications of the above models to statistics and engineering.