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UID:9089@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260519T143000
DTEND;TZID=Europe/Paris:20260519T153000
DTSTAMP:20260428T172500Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-301/
SUMMARY:Elisa MARINI (Université Paris Dauphine): Conditional propagation 
 of chaos for systems of interacting particles with simultaneous nearly-sta
 ble jumps
DESCRIPTION:Elisa MARINI: We consider a system of $N$ interacting particles
 \, described by SDEs driven by Poisson random measures\, where the coeffic
 ients depend on the empirical measure of the system. Every particle jumps 
 with a rate depending on its position. When this happens\, all the other p
 articles of the system receive a same random kick distributed according to
  a heavy-tailed random variable belonging to the domain of attraction of a
 n $\\alpha$-stable law and scaled by $N^{-1/\\alpha}$\, $\\alpha \\in (0\,
 2)\\setminus \\{1\\}$. We call these jumps collateral jumps. Moreover\, in
  case $0&lt\;\\alpha&lt\;1$\, the jumping particle itself undergoes a macr
 oscopic\, main jump. Similar systems are employed to model families of int
 eracting neurons and\, in that context\, main and collateral jumps represe
 nt respectively the hyperpolarization of a neuron after a spike and the sy
 naptic inputs received by post-synaptic neurons from pre-synaptic ones.  
 We prove that our system has the conditional propagation of chaos property
 : as $N\\to +\\infty$\, the finite particle system converges to an infinit
 e exchangeable system which obeys a McKean-Vlasov SDE driven by an $\\alph
 a$-stable process\, and particles in the limit system are independent\, co
 nditionally on the driving $\\alpha$-stable process. This talk is based on
  joint work with Eva L{\\"o}cherbach and Dasha Loukianova.
CATEGORIES:Séminaire,ALEA,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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