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UID:20251120T091705EST-1052zvIld0@132.216.98.100
DTSTAMP:20251120T141705Z
DESCRIPTION:Title: Arboreal structures on groups and the associated boundar
 ies - III\n\nAbstract: Geometers are very much used to endowing manifolds 
 with additional structures (Riemannian\, symplectic\, etc.). Likewise\, a 
 group can be equipped with a probability measure which gives rise to the a
 ssociated random walk (in the same way as a Riemannian metric gives rise t
 o the associated Brownian motion). This setup produces the Poisson boundar
 y as a measure space which describes the stochastically significant behavi
 our of the sample paths of the random walk at infinity.\n	\n	The Poisson bou
 ndary can usually be identified with the natural geometric boundary of the
  group (provided the latter is well-defined) endowed with an appropriate h
 itting distribution (e.g.\, for hyperbolic groups\, cf. the classical Pois
 son formula for the hyperbolic plane in the disk model). Still\, a number 
 of very natural questions about the identification of the Poisson boundary
  (or even just about its non-triviality) for general groups remain wide op
 en. It has been known for nearly 40 years that amenable groups can be char
 acterized as the ones for which there *exists* a measure with the trivial 
 Poisson boundary. According to a very recent result of Frisch - Hartman - 
 Tamuz - Vahidi Ferdowsi the hyper-FC-central groups are precisely those fo
 r which the boundary of *any* measure is trivial. The key ingredient of th
 is result is the existence of a measure with a non-trivial boundary on any
  group with infinite conjugacy classes (ICC). I will talk about a joint wo
 rk with Anna Erschler\, in which we introduce a new arboreal structure on 
 an arbitrary ICC group and subsequently identify the Poisson boundary in t
 erms of this structure.\n
DTSTART:20190426T180000Z
DTEND:20190426T190000Z
LOCATION:Room 4336\, CA\, Pav. André-Aisenstadt
SUMMARY:Vadim Kaimanovich\, Université d'Ottawa
URL:/mathstat/channels/event/vadim-kaimanovich-univers
 ite-dottawa-296384
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