We consider a large family of multiplicative statistics of eigenvalues of hermitian matrix models. We prove that they converge to an universal multiplicative statistics of the Airy2 point process which, in turn, is described in terms of a particular solution to the integro-differential Painlevé II equation (shortly int-diff PII). The same solution to this int-diff PII appeared for the first time in the description of the narrow wedge solution to the KPZ equation, so our results connect the KPZ equation in finite time with random matrix theory in an universal way.

We work under a one-cut regular assumption on the potential, and also under mild and natural assumptions on the multiplicative statistics. But as we also plan to explain, our approach indicates that families of integrable systems other than the int-diff PII may appear when considering multiplicative statistics associated with critical potentials.

The talk is based on joint work with Promit Ghosal (MIT).

A recording of the talk can be found here. Speaker(s): Guilherme Silva (Universidade de São Paulo)