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 bijectionis multiplication by a non-zero element of the finite field. This work is partially joint with Huy Pham and Max Xu.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
