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SUMMARY:Mixing time of random walk on dynamical random cluster - Alexandre
  Stauffer (King's College London)
DTSTART:20240708T143000Z
DTEND:20240708T153000Z
UID:TALK215563@talks.cam.ac.uk
DESCRIPTION:We consider a random walk jumping on a dynamic graph\; that is
 \, a graph that changes at the same time as the walker moves.&nbsp\;Previo
 us works considered the case where the graph changes via dynamical percola
 tion\, in which the edges of the graph switch between two states\, open an
 d closed\, and the walker is&nbsp\;only allowed to cross open edges. In dy
 namical percolation\, edges change their state independently of one anothe
 r.In this work\, we consider a graph dynamics with unbounded dependences: 
 Glauber dynamics on the random cluster model.We derive tight bounds on the
  mixing time when the density of open edges is small enough.&nbsp\;For the
  proof\, we construct a non-Markovian coupling using a multiscale analysis
  of the environment.This is based on joint work with Andrea Lelli.
LOCATION:Seminar Room 1\, Newton Institute
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