Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach
Mathematical Physics
2015-06-17 v1 math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1309.7015,
title = {Gap probabilities for the Generalized Bessel process: a Riemann-Hilbert approach},
author = {Manuela Girotti},
journal= {arXiv preprint arXiv:1309.7015},
year = {2015}
}
Comments
26 pages, 2 figures