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SUMMARY:The random walk on the exclusion process: a Law of Large numbers i
 n dimensions $\\geq 5$ - Guillaume Conchon--Kerjan (King's College London)
DTSTART:20260224T140000Z
DTEND:20260224T150000Z
UID:TALK243931@talks.cam.ac.uk
CONTACT:Pierre-François Rodriguez
DESCRIPTION:We study a random walk on the $d$-dimensional lattice ($d\\geq
  5$) whose (discrete-time) movements are randomly driven by an underlying 
 symmetric Simple Exclusion Process (SEP). In this set-up\, standard techni
 ques from static environments no longer apply. Moreover\, the SEP is conse
 rvative and induces long-range space-time correlations. With the loss of m
 onotonicity in dimensions above one\, only perturbative results have been 
 derived thus far. \nWe prove a law of large numbers in a wide regime of pa
 rameters. To do so\, we track the measure of the environment conditioned o
 n the past trajectory of the walker. This measure can be bounded in some s
 trong sense between two inhomogeneous products of Bernoulli measures\, tha
 t differ from the homogeneous one in a ‘summable’ way if the dimension
  is large enough. Joint work with Daniel Kious and Rémy Poudevigne.
LOCATION:MR12
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