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LA Probability Forum

Thursday, February 29, 2024
6:00pm to 7:00pm
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Superdiffusion for Brownian motion with random drift
Ahmed Bou-Rabee, Courant Institute of Mathematical Sciences, NYU,

UCLA, Math Sciences Room 6627

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.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at [email protected].