Riemann-Hilbert approach to gap probabilities for the Bessel process

Autor:	Girotti, Manuela
Rok vydání:	2013
Předmět:	Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1306.5663 Zobrazit plný text záznamu View this record from Arxiv