Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case

Details Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case

2011-04-26

arxiv.org/abs/1104.4940v1

Physics

Mathematical Physics

18 pages, 1 figure

Scientific paper

We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems, thus extending the known results for the single-time case. We focus on the Airy and Pearcey processes. As an example of applications we re-deduce a third order PDE, found by Adler and van Moerbeke, for the two-time Airy process.

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