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SUMMARY:Commuting probability in infinite groups  - Matthew Tointon (Unive
 rsity of Neuchâtel)
DTSTART:20171124T134500Z
DTEND:20171124T150000Z
UID:TALK94990@talks.cam.ac.uk
CONTACT:Maurice Chiodo
DESCRIPTION:In a finite group G one can ask what the probability is that t
 wo elements chosen independently uniformly at random commute. It is \nclea
 r that if G has an abelian subgroup of bounded index then this probability
  should be bounded from below. A beautiful theorem of Peter Neumann from t
 he 1980s shows that the converse is also true in a certain precise sense. 
 \n\nAntolin\, Martino and Ventura consider the same question for infinite 
 groups\, choosing the two random elements with respect to a certain limit 
 of finite probability measures. They conjecture that for any "reasonable" 
 sequence of measures Neumann's result should still hold. They also prove s
 ome special cases of this conjecture. \n\nIn this talk I will show that th
 e Antolin-Martino-Ventura conjecture holds with effective quantitative bou
 nds if we take the sequence of measures defined by the successive steps of
  a simple random walk\, or the uniform measures on a Folner sequence. I wi
 ll also present a concrete interpretation of the word "reasonable" that is
  sufficient to force a sequence of measures to obey the conjecture. If I h
 ave time I will present an application to conjugacy growth.
LOCATION:CMS\, MR13
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