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

Title:

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

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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