Seminar:
Analysis
Event time:
Thursday, September 26, 2024 - 4:00pm
Location:
KT 207
Speaker:
Ahmed Bou-Rabee
Event description:
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 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.
Research Area(s):
Analysis & PDE