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SUMMARY:Cutoff for Random Walk on Random Cayley Graphs - Sam Thomas (Stats
 lab)
DTSTART:20191022T130000Z
DTEND:20191022T140000Z
UID:TALK133336@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:Consider the random Cayley graph of a finite group G with resp
 ect 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 th
 ere exists a generator z so that g = hz or gz = h.\n\nA conjecture of Aldo
 us 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. \n\nTime permitting\, we discuss exte
 nsions 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 depe
 nds on the algebraic structure.\n\nJoint work with Jonathan Hermon
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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