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.
Riemann--Hilbert approach to multi-time processes: The Airy and the Pearcey cases / Bertola, M.; Cafasso, M.. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - 241:23-24(2012), pp. 2237-2245. [10.1016/j.physd.2012.01.003]
Riemann--Hilbert approach to multi-time processes: The Airy and the Pearcey cases
Bertola, M.;
2012-01-01
Abstract
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.| File | Dimensione | Formato | |
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