Mixing and cut-off for random walks on finite fields and random polynomials

I will report on joint work with Peter Varjú in which we investigate the ax+b random walk on a finite field F_p. Work from the 1990s by Chung-Diaconis-Graham established good upper bounds on mixing time when a=2. We refine their methods to understand the case when a is arbitrary in F_p. Using our previous work on irreducibility of polynomials of large degree, we obtain sharp bounds for the mixing time and prove, conditionally on the Generalized Riemann Hypothesis, that a sharp cut-off occurs.

• Speaker: Emmanuel Breuillard (Cambridge)
• Tuesday 04 February 2020, 14:00–15:00
• Venue: MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
• Series: Probability; organiser: Perla Sousi.