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UID:20250813T141414EDT-7866osHrjf@132.216.98.100
DTSTAMP:20250813T181414Z
DESCRIPTION:Title: The ICC property in random walks and dynamics.\n\nAbstra
 ct: A topological dynamical system (i.e. a group acting by homeomorphisms 
 on a compact Hausdorff space) is said to be proximal if for any two points
  $p$ and $q$ we can simultaneously 'push them together' (rigorously\, ther
 e is a net $g_n$ such that $\lim g_n(p) = \lim g_n(q)$). In his paper intr
 oducing the concept of proximality\, Glasner noted that whenever $\mathbb{
 Z}$ acts proximally\, that action will have a fixed point. He termed group
 s with this fixed point property “strongly amenable”. The Poisson boundary
  of a random walk on a group is a measure space that corresponds to the sp
 ace of different asymptotic trajectories that the random walk might take. 
 Given a group $G$ and a probability measure $\mu$ on $G$\, the Poisson bou
 ndary is trivial (i.e. has no non-trivial events) if and only if $G$ suppo
 rts a bounded $\mu$-harmonic function. A group is called Choquet–Deny if i
 ts Poisson boundary is trivial for every $\mu$. In this talk I will discus
 s work giving an explicit classification of which groups are Choquet–Deny\
 , which groups are strongly amenable\, and what these mysteriously equival
 ent classes of groups have to do with the ICC property. I will also discus
 s why strongly amenable groups can be viewed as strengthening amenability 
 in at least three distinct ways\, thus proving the name is extremely well 
 deserved.\n\nLink: https://mcgill.zoom.us/j/98910726246?pwd=VHlzTzdTZGtqcH
 VuWGNKdys4d0FzQT09\n\nZoom ID: 989 1072 6246\n	Password: delta\n
DTSTART:20210407T190000Z
DTEND:20210407T200000Z
SUMMARY:Joshua Frisch (California Institute of Technology)
URL:/mathstat/channels/event/joshua-frisch-california-
 institute-technology-330230
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