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Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 2012

Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases

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Résumé

We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels à 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.

Dates et versions

hal-03031621 , version 1 (30-11-2020)

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Marco Bertola, Mattia Cafasso. Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases. Physica D: Nonlinear Phenomena, 2012, 241 (23–24), pp.2237 - 2245. ⟨10.1016/j.physd.2012.01.003⟩. ⟨hal-03031621⟩
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