Probability Seminar - The tube property for the Swiss Cheese Problem
报告人：Dirk Erhard (Federal University of Bahia)
时间：2025-12-01 14:00-15:00
地点：智华楼-四元厅
Abstract: In 2001, Bolthausen, den Hollander, and van den Berg derived the asymptotics of the probability that the volume of a Wiener sausage at time t is smaller than its expected value multiplied by a small fixed constant. Their asymptotics were expressed through a variational formula, and they conjectured that the optimal strategy for such a large deviation event is for the underlying Brownian motion to display a "Swiss cheese" behavior: it should remain for most of the time inside a ball of subdiffusive size, visit most points within this ball, yet leave some random holes unvisited. They also conjectured that, in order to realize this strategy, the Brownian motion behaves like a Brownian motion in a drift field determined by the maximizer of the variational problem. In this talk, I will discuss the corresponding problem for the random walk and present results that support the conjectured picture.This is joint work with Julien Poisat.
Bio: Dirk Erhard completed his PhD in 2014 at Leiden University in the Netherlands under the supervision of Frank den Hollander. He then spent three years at the University of Warwick in the UK as a postdoctoral researcher working with Martin Hairer. In late 2017, he moved to Brazil to take up a professorship, and since then he has been a faculty member at the Federal University of Bahia. His research interests include interacting particle systems, large deviations, and singular stochastic partial differential equations.
