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SUMMARY:Convergence of Interacting Particle Systems toward Cross-Diffusion
  Equations
DTSTART:20260521T120000Z
DTEND:20260521T130000Z
DTSTAMP:20260502T152000Z
UID:indico-event-15372@indico.math.cnrs.fr
DESCRIPTION:Speakers: Vincent Bansaye\n\nWe consider spatially structured 
 populations that interact locally. More precisely\, two species move\, rep
 roduce\, and die at rates that depend on the local density of the other sp
 ecies\, that is\, on the number of individuals of the other species presen
 t at the same site. Our goal is to compare the empirical measure describin
 g the distribution of the two species with a deterministic cross-diffusion
  system (SKT-type PDEs)\, in the regime where both the number of sites and
  the local population sizes become large.\nThe main difficulty arises from
  the nonlinearity of the diffusion terms. Our approach relies on an interm
 ediate comparison with a semi-discrete system (an ODE system in dimension 
 2M\, where M is the number of sites). The results are based on the develop
 ment of quantitative stability estimates in this setting (duality lemmas)\
 , on the control of the associated martingales in Sobolev norms\, and on l
 arge deviation estimates for controlling birth and deaths.\nThis talk is b
 ased on joint works with Ayman Moussa\, Felipe Muñoz\, and Alexandre Bert
 olino.\n\nhttps://indico.math.cnrs.fr/event/15372/
LOCATION:435 (ENS de Lyon)
URL:https://indico.math.cnrs.fr/event/15372/
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