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SUMMARY:Mixing and cut-off for random walks on finite fields and random po
 lynomials - Emmanuel Breuillard (Cambridge)
DTSTART:20200204T140000Z
DTEND:20200204T150000Z
UID:TALK138637@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:I will report on joint work with Peter Varjú in which we inve
 stigate 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 deg
 ree\, we obtain sharp bounds for the mixing time and prove\, conditionally
  on the Generalized Riemann Hypothesis\, that a sharp cut-off occurs. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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