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UID:8873@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20251014T143000
DTEND;TZID=Europe/Paris:20251014T153000
DTSTAMP:20251003T075420Z
URL:https://www.i2m.univ-amu.fr/evenements/lln-and-clt-in-high-dimensions-
 for-the-random-walk-on-the-symmetric-exclusion-process/
SUMMARY:Rémy Poudevigne (LPSM): LLN and CLT in high dimensions for the ran
 dom walk on the symmetric exclusion process
DESCRIPTION:Rémy Poudevigne: The random walk on the exclusion process\nis 
 an example of random walk in dynamic environment.\nIn this specific model\
 ,\nthe law of the movement of the walker depends\non whether its current p
 osition is occupied\nby a particle or not.\nFurthermore\, the position of 
 the particles\nis given by a symmetric exclusion process (on $\\Z^d$).\nWh
 ile this dynamic is quite simple\,\nit has the inconvenient of being both\
 nconservative and slowly mixing\nwhich will cause strong correlations\nin 
 the position of the particles.\nIn dimension 1\, thanks to a monotonicity 
 property\,\nthe model is somewhat well understood\nbut in higher dimension
 s\nonly perturbative results are known.\nFor a wide range of parameters\,\
 nwe show that the walker satisfies\na law of large number in dimensions 5 
 and higher\nand a CLT in dimensions 9 and higher.\nFor this we look at the
  law of the environment\nknowing the trajectory of the walker\nand show th
 at it is not too far\nfrom the initial measure\, for any trajectory\,\nand
  conclude with standard tools for Markov chains.\nJoint work with Guillaum
 e Conchon-Kerjan and Daniel Kious.\n\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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