Multiplicative statistics of the Airy process and the Korteweg-de Vries equation

by Giulio Ruzza (Louvain-La-Neuve)

Location: online skype, Leuven
Time: Tuesday May 19, 2020 at 15:00

Based on a joint work in progress with Mattia Cafasso and Tom Claeys, we consider a novel class of solutions to the KdV equation, defined for \(t>0\) and blowing up at \(t=0\), arising in connection with a multiplicative statistics of the Airy point process. Such class can be regarded as a broad generalization of the classical self-similar KdV solution associated with the Ablowitz-Segur PII transcendent. In general, these solutions are instead connected with an integro-differential deformation of the PII equation; this deformation has been first found by Amir, Corwin, and Quastel in their study of the KPZ stochastic PDE with narrow wedge initial conditions.