|Location:||MSRI: Simons Auditorium, Online/Virtual|
Multiplicative Statistics For Eigenvalues Of Hermitian Matrix Models Are (KPZ) Universal
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We study the large matrix limit of a family of multiplicative statistics for eigenvalues of hermitian matrix models, showing that they universally connect with the integro-differential Painlevé II equation and, in turn, with the KPZ equation. But the connection does not stop there, and we will also explain how the norming constants of the associated orthogonal polynomials and the underlying correlation kernel are asymptotically described in terms of the same solution to the integro-differential PII. Although we work under the assumption of a regular one-cut potential and a family of multiplicative statistics satisfying certain regularity conditions, we also plan to discuss how our approach indicates that other classes of potentials may give rise to new families of integrable systems.
Based on ongoing work with Promit Ghosal (MIT).
Multiplicative Statistics for Eigenvalues of Hermitian Matrix Models are (KPZ) Universal