数学研究所
数学科学全国重点实验室
学术报告
偏微分方程研讨班
Speaker: Scott N. Armstrong（Sorbonne University）
Inviter: 阮国兴 副研究员
Language: English
Title:Anomalous diffusion and renormalization
Time&Venue: 2025年6月9日（星期一）16:00-17:00
& S813
Abstract:
I will discuss the large-scale/ long-time behavior of a Brownian particle advected by a random, incompressible (divergence-free) vector field. If this vector field has correlations which decay with a critical exponent (which happens to be -2), then the behavior of the particle is superdiffusive instead of diffusive. In particular, after time 
, the particle will be on average a distance of 
from its starting point. This phenomenon was explained in the physics literature in the late 1980s as a build-up of diffusivity across many length scales, using renormalization group arguments. I will discuss recent mathematical innovations based on analytic ideas that allow us to make these renormalization group arguments rigorous. (This is joint work with A. Bou-Rabee and T. Kuusi.)
