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
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.
For more information, and how to access the seminar through Zoom, see the webpage of the events here.