The eigenvalues of large random matrices are known to describe the limiting behaviors of various objects in mathematics, statistics and physics such as random permutations, zeros of Riemann-zeta function, sample covariance matrices, non-intersecting paths and random growth models. The investigator plans to study various intrinsic properties the limiting distribution functions arising in random matrix theory, as well as to apply the ideas and methods of random matrix theory to probability models such as last passage percolation, queueing models, non-intersecting paths and interacting particle systems. Built on the investigator's and other researchers' earlier work, the long term goal is to clarify the universality class of models which are describable in terms of the eigenvalues of random matrices using ideas from both integrable systems and probability.
