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arXiv · 1612.02321

Interlacing adjacent levels of $β$--Jacobi corners processes

Vadim Gorin·Lingfu Zhang
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Abstract

We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the $β$--Jacobi corners process (multilevel and general $β$ extension of the classical Jacobi ensemble of random matrices). The limit is identified with the derivative of the $2d$ Gaussian Free Field. Our main tools are integral forms for the (Macdonald-type) difference operators originating from the shuffle algebra.

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Vadim Gorin, Lingfu Zhang. 2017-12-24. Interlacing adjacent levels of $β$--Jacobi corners processes. https://arxiv.org/abs/1612.02321

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