Scaling Distribution of the Multiple Range of a 1-D Random Walk up to Time of Exit
Mathematical Physics and Probability Seminar
Scaling Distribution of the Multiple Range of a 1-D Random Walk up to Time of Exit
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Conner Hatton, University of Arizona
The range and multiple range of a random walk up to time n specify the numbers of points visited at all and those visited exactly k times up to time n, respectively. Such quantities for fair and other types of random walks on Z^d have been classically studied. Less is known when the random walk is constrained in some way. Previous work has studied the range and multiple range up to the time exit from domains in Z^d, mostly when d>1. In particular, the behavior of the multiple range in the d=1 setting seems less explored. In this talk, we consider in d=1 the multiple range of simple symmetric random walk up to the time of exit from an interval 1,2, ... , N., in particular their scaling limits.
(https://arizona.zoom.us/j/87802949465)