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arXiv · 1306.5663

Riemann-Hilbert approach to gap probabilities for the Bessel process

Manuela Girotti
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Abstract

We consider the gap probability for the 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 integrable kernels \`a la Its-Izergin-Korepin-Slavnov and thus related to suitable Riemann-Hilbert problems. In the single-time case, we construct a Lax pair formalism and we derive a Painlev\'e III equation related to the Fredholm determinant.

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Manuela Girotti. 2013-06-24. Riemann-Hilbert approach to gap probabilities for the Bessel process. https://arxiv.org/abs/1306.5663

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