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SUMMARY:The point of view of the particle for 2D random walks in Dirichlet
  environment - Christophe Sabot (Université Claude Bernard Lyon 1)
DTSTART:20240712T081500Z
DTEND:20240712T091500Z
UID:TALK215608@talks.cam.ac.uk
DESCRIPTION:Random Walks in random Dirichlet Environment (RWDE) is the mod
 el of random walks in random environment with i.i.d. Dirichlet distributed
  transition probabilities at each site. With this specific choice of envir
 onment the annealead law is the directed Edge Reinforced Random Walk. Besi
 des\, under some condition on the weights the time-reversed walk is again 
 a RWDE. This was used e.g. in dimension d>2\, to prove the existence of an
  invariant measure for the process viewed from the particle\, absolutely c
 ontinuous with respect to the static law. We will present a new identity f
 or RWDE\, inspired by the Vertex Reinforced Jump Process (VRJP)\, more pre
 cisely by its non-reversible generalization\, the *-VRJP. From this identi
 ty we will deduce some sufficient conditions in 2D for the existence or no
 n-existence of an absolutely continuous invariant measure for the process 
 viewed from the particle.\nJoint with Adrien Perrel.
LOCATION:Seminar Room 1\, Newton Institute
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