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SUMMARY:Parthanil Roy (Indian Statistical Institute\, Bangalore)
DTSTART:20200812T100000Z
DTEND:20200812T104500Z
DTSTAMP:20260404T172051Z
UID:BPS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BPS/3
 /">Group measure space construction\, ergodicity and superrigidity for sta
 ble random fields</a>\nby Parthanil Roy (Indian Statistical Institute\, Ba
 ngalore) as part of Bangalore Probability Seminar\n\n\nAbstract\nIn this w
 ork\, it is established that the group measure space construction correspo
 nding to a minimal representation is an invariant of a stationary symmetri
 c $\\alpha$-stable (S$\\alpha$S) random field indexed by any countable gro
 up $G$. When $G=\\mathbb{Z}^d$\, we characterize ergodicity of stationary 
 S$\\alpha$S fields in terms of the central decomposition of this crossed p
 roduct von Neumann algebra coming from any (not necessarily minimal) Rosin
 ski representation. This shows that ergodicity is a $W^*$-rigid property (
 in a suitable sense) for this class of fields. All our results have analog
 ues for stationary max-stable random fields as well.\n
LOCATION:https://stable.researchseminars.org/talk/BPS/3/
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