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SUMMARY:Mixing of a random walk on a randomly twisted hypercube - Zsuzsa B
 aran (Cambridge)
DTSTART:20250520T130000Z
DTEND:20250520T140000Z
UID:TALK232534@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION: We consider `randomly twisted hypercubes'\, i.e.\\ random gra
 phs $G^{(n)}$ for $n\\ge0$ that can be defined recursively as follows. Let
  $G^{(0)}$ be a graph consisting of a single vertex\, and for $n\\ge1$ let
  $G^{(n)}$ be obtained by considering two independent copies $G^{(n-1\,1)}
 $ and $G^{(n-1\,2)}$ of $G^{(n-1)}$ and adding the edges corresponding to 
 a uniform random matching between their vertices.\nWe study a lazy or simp
 le random walk on these and in both cases establish that their mixing time
 s are of order $n$ and they do not exhibit cutoff. In this talk I hope to 
 have enough time to discuss this model and the results and also present mo
 st of the ideas of the proofs.\nJoint work with An{\\dj}ela \\v{S}arkovi\\
 'c\; based on a joint work with Jonathan Hermon\, An{\\dj}ela \\v{S}arkovi
 \\'c\, Allan Sly and Perla Sousi.\n
LOCATION:MR12
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