Riemann-Hilbert approach to gap probabilities for the Bessel process
Autor: | Girotti, Manuela |
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Rok vydání: | 2013 |
Předmět: | |
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 |
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