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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