Article ID Journal Published Year Pages File Type
8256399 Physica D: Nonlinear Phenomena 2015 19 Pages PDF
Abstract
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.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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