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arXiv · 2308.14707

On the hard edge limit of the zero temperature Laguerre beta corners process

Matthew Lerner-Brecher
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Abstract

We study the hard edge limit of a multilevel extension of the Laguerre $\beta$-ensemble at zero temperature. In particular, we show that asymptotically the ensemble is given by Gaussians with covariance matrix expressible in terms of the Fourier-Bessel series. These Gaussians also have an explicit representation as the partition functions of additive polymers arising from a random walk on roots of the Bessel functions. Our approach builds off of the one introduced in arxiv:2009.02006 and is rooted in using the theory of dual and associated polynomials to diagonalize transition matrices relating levels of the ensemble.

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Matthew Lerner-Brecher. 2023-08-28. On the hard edge limit of the zero temperature Laguerre beta corners process. https://arxiv.org/abs/2308.14707

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