Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes

Jinho Baik; Zhipeng Liu

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arXiv · 1212.4467

Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes

Jinho Baik·Zhipeng Liu

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Abstract

We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This identity is used to evaluate a triple asymptotic of some discrete Toeplitz/Hankel determinants which arise in studying non-intersecting processes. We show that the asymptotic fluctuations of the width of such processes are given by the GUE Tracy-Widom distribution. This result leads us to an identity between the GUE Tracy-Widom distribution and the maximum of the sum of two independent Airy processes minus a parabola. We provide an independent proof of this identity.

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BibTeX RIS

Jinho Baik, Zhipeng Liu. 2013-05-17. Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes. https://arxiv.org/abs/1212.4467

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