Bertola, Marco and Cafasso, M. (2012) Riemann-Hilbert approach to multi-time processes: The Airy and the Pearcey cases. Physica D: Nonlinear Phenomena, 241 (23-24). pp. 2237-2245. ISSN 01672789
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Official URL: http://dx.doi.org/10.1016/j.physd.2012.01.003
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.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Article |
| Refereed: | Yes |
| Authors: | Bertola, Marco and Cafasso, M. |
| Journal or Publication: | Physica D: Nonlinear Phenomena |
| Date: | 2012 |
| Digital Object Identifier (DOI): | 10.1016/j.physd.2012.01.003 |
| Keywords: | Random point processes; Riemann–Hilbert problems; Integrable kernels |
| ID Code: | 976937 |
| Deposited By: | Danielle Dennie |
| Deposited On: | 05 Mar 2013 16:12 |
| Last Modified: | 18 Jan 2018 17:43 |
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