Gap Probability for the Hard Edge Pearcey Process

Dai Dan; Xu Shuai-Xia; Zhang Lun

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Gap Probability for the Hard Edge Pearcey Process

机译：Gap Probability for the Hard Edge Pearcey Process

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The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval (0, s) by working on a 3 x 3 matrix-valued Riemann-Hilbert problem for the relevant Fredholm determinants. We establish an integral representation of the gap probability via the Hamiltonian related to a new system of coupled differential equations. Together with some remarkable differential identities for the Hamiltonian, we derive the large gap asymptotics for the thinned hard edge Pearcey process, including the explicitly evaluation of the constant factor in terms of the Barnes G-function. As an application, we also obtain the asymptotic statistical properties of the counting function for the hard edge Pearcey process.

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来源
《Annales Henri Poincare》 |2023年第6期|2067-2136|共70页
作者
Dai Dan; Xu Shuai-Xia; Zhang Lun;
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作者单位

City Univ Hong Kong;

Sun Yat Sen Univ;

Fudan Univ;

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正文语种英语
中图分类理论物理学;
关键词
LEVEL-SPACING DISTRIBUTIONS; SQUARED BESSEL PATHS; ORTHOGONAL POLYNOMIALS; RANDOM MATRICES; ASYMPTOTICS; AIRY; DETERMINANT; GROWTH; MODELS; LIMIT;

Gap Probability for the Hard Edge Pearcey Process

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