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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20220429T083021Z
DTSTART:20220504T140000Z
DTEND:20220504T150000Z
SUMMARY:Pierre Patie -  Discrete self-similarity and  some ergodic Markov
  chains
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}j1m5-l2k6d2
 h8-93z7w2
DESCRIPTION:Pierre Patie (Cornell University) will speak in the Probabili
 ty seminar. \n\nIn this talk\, resorting to the theory of group represen
 tation\, we start by introducing an operator that defines the concept of
  discrete self-similarity\, that is a scaling on a lattice. We proceed b
 y identifying\, by means of their generator\, the class of Markov chains
  which are semi-invariant by this group action\, and call them discrete 
 self-similar Markov chains.  We show that they belong to the domain of a
 ttraction of a subclass of the Lamperti  (continuous) self-similar Marko
 v processes on the positive real line.  More interestingly\, it turns ou
 t that the corresponding semigroups of the continuous and discrete versi
 ons satisfy a so-called gateway relation\, revealing that scaling limit 
 may be substitute  to a (pseudo-) isomorphism between these operators. W
 e explain why this unexpected fact is\, in fact\, natural.  This gateway
  relation is preserved when one considers the ergodic companions of thes
 e non-reversible Markov processes. We combined this fact with some addit
 ional classification schemes  that we have proposed recently to obtain s
 everal substantial analytical and ergodic properties of the discrete ver
 sion such as the spectral properties\, entropy decay\, hypercoercivity a
 nd hypercontractivity.  We emphasize that all these properties for the d
 iscrete version are transferred from the continuous analogue (the scalin
 g limit)\, which is somehow unusual.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:https://zoom.us/j/95434478825
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