Random matrix models arising from projections of orbital measures

Abstract: A number of widely studied random matrix models can be realized as projections of invariant measures on group orbits. Examples include the randomized Horn's problem, the randomized Schur's problem, and the orbital corners process. In this talk we will introduce a general framework that unifies these models in the case of coadjoint orbits of a compact Lie group. We will present both recent and classical results that hold in this general setting, and we will discuss applications to combinatorial representation theory and quantum information theory. The talk will be accessible to probabilists without a background in Lie theory or representation theory. Results presented will include joint work with Jean-Bernard Zuber, Robert Coquereaux, and Benoît Collins.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .