MIT Probability Seminar
Monday, September 13, 2021 at 4:00pm to 5:30pm
Building 2, Room: 2-147
182 MEMORIAL DR, Cambridge, MA 02139
Title: Random walks on finite fields with deterministic jumps
Abstract: Recently, Chatterjee and Diaconis showed that most bijections, if applied between steps of a Markov chain, cause the resulting chain to mix much faster. However, explicit examples of this speedup phenomenon are rare. I will discuss recent work studying such walks on finite fields where the bijection is algebraically defined. This work gives a large collection of examples where this speedup phenomenon occurs. These walks can be seen as a non-linear analogue of the Chung-Diaconis-Graham process, where the bijection is multiplication by a non-zero element of the finite field. This work is partially joint with Huy Pham and Max Xu.