Fredholm determinants, exact solutions to the Kardar-Parisi-Zhang equation and integro-differential Painlevé equations

Abstract: As Fredholm determinants are more and more frequent in the context of stochastic integrability, I discuss in this talk the existence of a common framework in many integrable systems where they appear. This consists in a hierarchy of equations, akin to the Zakharov-Shabat system, connecting an integro-differential extension of the Painlevé II hierarchy, the finite-time solutions of the Kardar-Parisi-Zhang equation and multi-critical fermions at finite temperature. The talk is based on the results of the paper arXiv:2008.01509

statistical mechanicsmathematical physicsprobability

Audience: researchers in the topic

Séminaire MEGA

Series comments: Description: Monthly seminar on random matrices and random graphs