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Random matrix central limit theorems for nonintersecting random walks

Jinho Baik·Toufic M. Suidan
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Abstract

We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.

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Jinho Baik, Toufic M. Suidan. 2006-05-08. Random matrix central limit theorems for nonintersecting random walks. https://doi.org/10.1214/009117906000001105

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