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UID:8700@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250624T143000
DTEND;TZID=Europe/Paris:20250624T153000
DTSTAMP:20250620T203148Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-238/
SUMMARY:Rémy Poudevigne (...): LLN and CLT in high dimensions for the rand
 om walk on the symmetric exclusion process
DESCRIPTION:Rémy Poudevigne: The random walk on the exclusion process is a
 n example of random walk in\ndynamic environment. In this specific model\,
  the law of the movement of the\nwalker depends on whether its current pos
 ition is occupied by a particle or\nnot. Furthermore\, the position of the
  particles is given by a symmetric\nexclusion process (on $\\Z^d$). While 
 this dynamic is quite simple\, it has\nthe inconvenient of being both cons
 ervative and slowly mixing which will\ncause strong correlations in the po
 sition of the particles. In dimension 1\,\nthanks to a monotonicity proper
 ty\, the model is somewhat well understood\nbut in higher dimensions only 
 perturbative results are known. For a wide\nrange of parameters\, we show 
 that the walker satisfies a law of large\nnumber in dimensions 5 and highe
 r and a CLT in dimensions 9 and higher. For\nthis we look at the law of th
 e environment knowing the trajectory of the\nwalker and show that it is no
 t too far from the initial measure\, for any\ntrajectory and conclude with
  standard tools for Markov chains.\nJoint work with Guillaume Conchon-Kerj
 an and Daniel Kious.\n
CATEGORIES:Séminaire,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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DTSTART:20250330T030000
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