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

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.

26 pages, 2 figures

References in corpus (4)

• Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
• Non-intersecting squared Bessel paths: critical time and double scaling limit
• Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case
• Riemann-Hilbert approach to gap probabilities for the Bessel process

Cited by in corpus (6)

• Universality conjecture and results for a model of several coupled positive-definite matrices
• The hard edge tacnode process and the hard edge Pearcey process with non-intersecting squared Bessel paths
• Gap probability for the hard edge Pearcey process
• A Riemann Hilbert approach to the study of the generating function associated to the Pearcey process
• Gap probability for products of random matrices in the critical regime
• Gap probability at the hard edge for random matrix ensembles with pole singularities in the potential