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arXiv · 1309.7015

Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach

Manuela Girotti
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Abstract

We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case. We prove that the scalar and matrix Fredholm determinants of such process can be expressed in terms of determinants of Its-Izergin-Korepin-Slavnov integrable kernels and thus related to suitable Riemann-Hilbert problems. In the single-time case, we construct a Lax pair formalism, while in the multi-time case we explicitly define a new multi-time kernel to study.

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Manuela Girotti. 2013-09-26. Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach. https://doi.org/10.1007/s11040-014-9149-2

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