Random matrices and interacting particle systems

Content: For Hermitian random matrices the distribution of the largest eigenvalue converges, in the limit of large size, to the so-called Tracy-Widom distribution function. This distribution describes also the fluctuations of a particle in the asymmetric simple exclusion process in the large time limit. This is at first surprising since the two models are very different and a-priori do not have anything in common. In this series of lectures we will focus in explaining where the (partial) connection between the fields of random matrices and interacting particle systems arise.

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