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## Cutoff for Random Walk on Random Cayley GraphsAdd to your list(s) Download to your calendar using vCal - Sam Thomas (Statslab)
- Tuesday 22 October 2019, 14:00-15:00
- MR12, CMS, Wilberforce Road, Cambridge, CB3 0WB.
If you have a question about this talk, please contact Perla Sousi. Consider the random Cayley graph of a finite group G with respect to k generators chosen uniformly at random, with 1 << log k << log|G|: the vertices are the group elements, and g, h in G are connected if there exists a generator z so that g = hz or gz = h. A conjecture of Aldous and Diaconis asserts that the simple random walk on this graph exhibits cutoff, at a time which depends only on |G| and k, not on the algebraic structure of the group G (ie universally in G). We verify this conjecture for a wide class of Abelian groups. Time permitting, we discuss extensions to the case where the underlying group G is non-Abelian. There the cutoff time cannot be written only as a function of |G| and of k; it depends on the algebraic structure. Joint work with Jonathan Hermon This talk is part of the Probability series. ## This talk is included in these lists:- All CMS events
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