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SUMMARY:Volume growth\, random walks and electric resistance in vertex-tra
 nsitive graphs - Matthew Tointon (University of Cambridge)
DTSTART:20191113T134500Z
DTEND:20191113T144500Z
UID:TALK132850@talks.cam.ac.uk
CONTACT:Thomas Bloom
DESCRIPTION:An infinite connected graph G is called recurrent if\, with pr
 obability 1\, the simple random walk on G it eventually returns to its sta
 rting point. Varopoulos famously showed that a Cayley graph has a recurren
 t random walk if and only if the underlying group has a finite-index subgr
 oup isomorphic to 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 t
 he ball of radius n about the identity grows at most quadratically in n. I
 n this talk I will describe some finitary versions of these statements. In
  particular\, I will present an analogue of Varopoulos's theorem for finit
 e Cayley graphs\, resolving a conjecture of Benjamini and Kozma. This is j
 oint work with Romain Tessera.
LOCATION:MR5\, CMS
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