Probability and Stochastic Analysis Seminar  RSS

02/06/2021, 17:00 — 18:00 — Online
, Institut de Mathématiques de Toulouse

Kahane's Gaussian Multiplicative Chaos and Circular Random Matrices match exactly

In this talk, I would like to advertise the strict equality between two objects from very different areas of mathematical physics:

  • Kahane's Gaussian Multiplicative Chaos (GMC), which uses a log-correlated field as input and plays an important role in certain conformal field theories
  • A reference model in random matrices called the Circular Beta Ensemble (CBE).

The goal is to give a precise theorem whose loose form is GMC = CBE. Although it was known that random matrices exhibit log-correlated features, such an exact correspondence is quite a surprise.

link

Except for a few of the oldest sessions these are from the Seminário de Probabilidade e Mecânica Estatística at IMPA which is co-sponsored by several institutions, in particular Instituto Superior Técnico.