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DTSTART:19700329T010000
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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Volume growth\, random walks and electric resistan
ce in vertex-transitive graphs - Matthew Tointon (
University of Cambridge)
DTSTART;TZID=Europe/London:20191113T134500
DTEND;TZID=Europe/London:20191113T144500
UID:TALK132850AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/132850
DESCRIPTION:An infinite connected graph G is called recurrent
if\, with probability 1\, the simple random walk o
n G it eventually returns to its starting point. V
aropoulos famously showed that a Cayley graph has
a recurrent random walk if and only if the underly
ing group has a finite-index subgroup isomorphic t
o Z or Z^2. A key step is to show that a recurrent
Cayley graph has at most quadratic volume growth
- that is\, the cardinality of the ball of radius
n about the identity grows at most quadratically i
n n. In this talk I will describe some finitary ve
rsions of these statements. In particular\, I will
present an analogue of Varopoulos's theorem for f
inite Cayley graphs\, resolving a conjecture of Be
njamini and Kozma. This is joint work with Romain
Tessera.
LOCATION:MR5\, CMS
CONTACT:Thomas Bloom
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