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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-185
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:MATTHEW WIERSMA\, UNIVERSITY OF WATERLOO\n\n_Entropies and Pois
 son boundaries of random walks on groups with rapid\ndecay_\n\nLet $G$ be 
 a countable group and $\\mu$ a probability measure on $G$.\nThe Avez entro
 py of $\\mu$ provides a way of quantifying the randomness\nof the random w
 alk on $G$ associated with $\\mu$. We build a new\nframework to compute as
 ymptotic quantities associated with the\n$\\mu$-random walk on $G$\, using
  constructions that arise from harmonic\nanalysis on groups. We introduce 
 the notion of \\emph{convolution\nentropy} and show that\, under mild assu
 mptions on $\\mu$\, it coincides\nwith the Avez entropy of $\\mu$ when $G$
  has the rapid decay property.\nSubsequently\, we apply our results to sta
 tionary dynamical systems\nconsisting of an action of a group with the rap
 id decay property on a\nprobability space\, and give several characterizat
 ions for when the\nAvez entropy coincides with the Furstenberg entropy of 
 the stationary\nspace. This leads to a characterization of Zimmer amenabil
 ity for\nstationary dynamical systems whenever the acting group has the\np
 roperty of rapid decay.\n\nThis talk is based on joint work with B. Anders
 on-Sackaney\, T. de Laat\nand E. Samei.\n\nMC 5417 or Zoom link below\n\nh
 ttps://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT0
 9
DTSTAMP:20260504T231241Z
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