Probability and Mathematical Physics Seminar
Probability and the City Seminar (at Columbia)
Speaker: Kavita Ramanan (Brown) and Kevin Hu (Columbia)
Location: Columbia University, Mathematics Hall, 2990 Broadway
Date: Friday, December 5, 2025, 11 a.m.
Synopsis:
Speaker: Kavita Ramanan (Brown)
Title: The Rademacher phase of the unitary group and some consequences
Abstract: It is well documented that high-dimensional random matrices distributed according to Haar measure on the unitary group behave in many ways like matrices with independent and identically distributed (i.i.d.) complex Gaussian entries. We describe complementary results that identify a transition in which a Rademacher phase emerges. Time permitting, we will also describe how such a result is useful for probing the geometry of p-Schatten spaces, and answering an open question of V. Milman in this context. This is based on joint work with G. Paouris.
Speaker: Kevin Hu (Columbia)
Title: Quantitative unimodular propagation of chaos
Abstract: Propagation of chaos, which is commonly studied in the context of mean-field interacting particle systems, describes the asymptotic independence of particles in the infinite-population limit. It was recently shown by Lacker, Ramanan, and Wu, that random pairs of particles in strongly interacting particle systems on sparse graphs become asymptotically independent as well. In this talk I will discuss recent work on quantitative estimates for this phenomenon, which we refer to as unimodular propagation of chaos. The proof utilizes coupling estimates for random graphs as well as a surprising connection between propagation of chaos and first-passage percolation. This is joint work with Kavita Ramanan and Dan Lacker.