Probability Seminar: Fluctuation results for size of the vacant set for random walks on discrete torus
- Event Type
- Seminar/Symposium
- Sponsor
- Math Department
- Location
- 347 Altgeld Hall
- Date
- Oct 26, 2021 2:00 pm
- Speaker
- Daesung Kim
- Contact
- Daesung Kim
- daesungk@illinois.edu
- Views
- 11
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.