Stanislav Volkov: Rademacher Random Walk

Abstract: Consider a random walk whose step sizes depend on the current time. Although such a process might appear easier to analyse than, for example, path-dependent random walks (e.g., reinforced random walks), it still exhibits many intriguing phenomena. For example, a variant of the simple symmetric one-dimensional random walk in which the step size at time n is exactly n is transient - a fact that is far from obvious.

In this talk, I will discuss variations of such processes in both one and higher dimensions. The results I will present are based in part on joint work with my PhD student, Dr. Satyaki Bhattacharya, who recently defended his thesis.