Random Matrices and Applications

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AbstractBaikThe eigenvalues of large random matrices are known to describe thelimiting behaviors of various objects in mathematics, statisticsand physics such as random permutations, zeros of Riemann-zetafunction, sample covariance matrices, non-intersecting paths andrandom growth models. The investigator plans to study variousintrinsic properties the limiting distribution functions arisingin random matrix theory, as well as to apply the ideas and methodsof random matrix theory to probability models such as last passagepercolation, queueing models, non-intersecting paths andinteracting particle systems. Built on the investigator's andother researchers' earlier work, the long term goal is to clarifythe universality class of models which are describable in terms ofthe eigenvalues of random matrices using ideas from bothintegrable systems and probability.