Probability and Statistics Seminar: Random walks on finite fields with deterministic jumps

Friday, January 22 at 3:30pm to 4:30pm

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Jimmy He, Stanford University

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, and give a near-linear mixing time. 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.

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