Riemann-Hilbert approach to gap probabilities for the Bessel process

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 à 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 Painlevé III equation related to the Fredholm determinant.

28 pages, 3 figures

References in corpus (1)

• Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case

Cited by in corpus (1)

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