University of Cambridge > > Probability > Cutoff for Random Walk on Random Cayley Graphs

Cutoff for Random Walk on Random Cayley Graphs

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity