Evolution of the Stochastic Airy eigenvalues under a changing boundary

2020/02/27 by Gonzalez, Angelica, Holcomb, Diane
#60B20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2002.12191

Abstract

The Airy_β point process, originally introduced by Ramírez, Rider, and Virág, is defined as the spectrum of the stochastic Airy operator H_β acting on a subspace of L²[0,∞) with Dirichlet boundary condition. In this paper we study the coupled family of point processes defined as the eigenvalues of H_β acting on a subspace of L²[t,∞). These point processes are coupled through the Brownian term of H_β. We show that these point processes as a function of t are differentiable with explicitly computable derivative. Moreover when recentered by t the resulting point process is stationary. This process can also be viewed as an analogue to the 'GUE minor process' in the tridiagonal setting.

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