VIRTUAL SEMINAR SERIES -- INTEGRABLE SYSTEMS: Airy kernel determinant solutions of the KdV equation

Tom Claeys (Université Catholique de Louvain)

Wednesday 10th November, 2021 13:30-14:30 Zoom seminar hosted by ICMS

Abstract

Deformed Airy kernel Fredholm determinants characterize the narrow wedge solution of the Kardar-Parisi-Zhang equation, and appear as largest particle distribution in models of finite temperature free fermions. From the integrable systems point of view, these determinants are rich objects, which generate a family of solutions to the KdV equation, and which are connected to an integro-differential Painleve II equation. These KdV solutions are singular as $t\to 0$, and their small time asymptotics are the key to obtaining tail probabilities for the narrow wedge solution of the Kardar-Parisi-Zhang equation. Based on joint works with Mattia Cafasso, Giulio Ruzza, and Christophe Charlier.

 

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