Some Aspects of Random Matrices and Integrable Systems

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The aim of this proposal is to study various aspects of random matrix theory and integrable systems. One pat of the project is to study asymptotic properties of various distribution functions arising in random matrix theory using their connection to integrable systems. Another part of the project concerns on the universality questions. These are motivated by problems in statistics and integrable differential equations. The long term goal is to understand a clear picture of the universality property of random matrix theory. Random matrix theory describes a wide array of objects in mathematics such as number theory, combinatorics, probability, as well as in other disciplines of science like statistics, physics, economics, finance and electrical engineering. This proposal is aimed to study some intrinsic properties of random matrices motivated from such applications to improve our understanding of the field.