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- W3007000487 abstract "The Airy$_beta$ point process, originally introduced by Ramirez, Rider, and Virag, is defined as the spectrum of the stochastic Airy operator $mathcal{H}_beta$ acting on a subspace of $L^2[0,infty)$ with Dirichlet boundary condition. In this paper we study the coupled family of point processes defined as the eigenvalues of $mathcal{H}_beta$ acting on a subspace of $L^2[t,infty)$. These point processes are coupled through the Brownian term of $mathcal{H}_beta$. 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." @default.
- W3007000487 created "2020-03-06" @default.
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- W3007000487 date "2020-02-27" @default.
- W3007000487 modified "2023-10-01" @default.
- W3007000487 title "Evolution of the Stochastic Airy eigenvalues under a changing boundary" @default.
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