Fluctuation results for size of the vacant set for random walks on discrete torus

Stochastics Seminar
Thursday, November 3, 2022 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Daesung Kim – Georgia Tech
Cheng Mao

We consider a random walk on the $d\ge 3$ dimensional discrete torus starting from vertices chosen independently and uniformly at random. In this talk, we discuss the fluctuation behavior of the size of the range of the random walk trajectories at a time proportional to the size of the torus. The proof relies on a refined analysis of tail estimates for hitting time. We also discuss related results and open problems. This is based on joint work with Partha Dey.