Riemann-Hilbert approach to gap probabilities for the Bessel process

Girotti, Manuela
(2015) Physica D: Nonlinear Phenomena — Vol. 1, n° 1, p. 1-35 (2015)

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  • Girotti, ManuelaUCLouvain
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Abstract
(en) 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 in the sense of 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.
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Girotti, M. (2015). Riemann-Hilbert approach to gap probabilities for the Bessel process. Physica D: Nonlinear Phenomena, 1(1), 1-35. https://doi.org/10.1016/j.physd.2014.12.009 (Original work published 2015)