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SUMMARY:Thick Points of Random Walk and the Gaussian Free Field - Antoine 
 Jego (Cambridge Centre for Analysis)
DTSTART:20180718T083500Z
DTEND:20180718T085500Z
UID:TALK108346@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We consider the thick points of random walk\, i.e. points wher
 e the local time is a fraction of the maximum. In two dimensions\, we answ
 er a question of Dembo\, Peres\, Rosen and Zeitouni and compute the number
  of thick points of planar random walk\, assuming that the increments are 
 symmetric and have a finite moment of order two. The proof provides a stre
 amlined argument based on the connection to the Gaussian free field and wo
 rks in a very general setting including isoradial graphs. In higher dimens
 ions\, we show that the number of thick points converges to a nondegenerat
 e random variable and that the maximum of the local times converges to a r
 andomly shifted Gumbel distribution.  <br><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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