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

M. Bertola; M. Cafasso

doi:10.1016/j.physd.2012.01.003

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

Mathematical Physics 2013-06-06 v1 math.MP Probability Exactly Solvable and Integrable Systems

Authors: M. Bertola , M. Cafasso

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Abstract

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.

Keywords

Riemann-Hilbert problem multi-time processes Airy process Pearcey process Fredholm determinant integrable kernels IIKS

Cite

@article{arxiv.1104.4940,
  title  = {Riemann-Hilbert approach to multi-time processes; the Airy and the Pearcey case},
  author = {M. Bertola and M. Cafasso},
  journal= {arXiv preprint arXiv:1104.4940},
  year   = {2013}
}

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18 pages, 1 figure

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

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Keywords

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