# Probability and Mathematical Physics Seminar

#### Superdiffusion for Brownian motion with random drift

**Speaker:**
Ahmed Bou-Rabee, NYU

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, April 12, 2024, 11:10 a.m.

**Synopsis:**

A Brownian particle subject to a random, divergence-free drift will have enhanced diffusion. The correlation structure of the drift determines the strength of the diffusion and there is a critical threshold, bordering the diffusive and superdiffusive regimes. Physicists have long expected logarithmic-type superdiffusivity at this threshold, and recently some progress in this direction has been made by mathematicians.

I will discuss joint work [arXiv:2404.01115] with Scott Armstrong and Tuomo Kuusi in which we identify and obtain the sharp rate of superdiffusivity. We also establish a quenched invariance principle under this scaling. Our proof is a quantitative renormalization group argument made rigorous by ideas from stochastic homogenization.