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SUMMARY:The Porous Medium Equation: Multiscale Analysis of a Zero-Range Pr
 ocess\, Integrability Estimate and Large Deviations - Daniel Heydecker (Im
 perial College)
DTSTART:20250506T130000Z
DTEND:20250506T140000Z
UID:TALK231106@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We consider a doubly-rescaled zero-range process with jump rat
 e $g(k)=k^\\alpha\, \\alpha>1$\, with scaling parameters $\\chi_N\\to 0\, 
 N\\to \\infty$\, as a microscopic model for the porous medium equation. As
  a result of the superlinear jump rate\, new ingredients are needed in add
 ition to the Kipnis-Landim framework\, of which the most interesting is an
  integrability estimate: Even if one can prove rapid equilibration on macr
 oscopically small boxes\, the superexponential estimate could fail due to 
 configurations in which a vanishing proportion of mass produces a nonvanis
 hing contribution to the $L^\\alpha_{t\,x}$ norm. In order to rule this ou
 t\, we show that the realisations of the particle system enjoy pathwise re
 gularity estimates with superexponentially high probability across suitabl
 y chosen scales\, which can be used in a multiscale argument to obtain the
  necessary integrability. Joint work with Benjamin Gess (TU Berlin / Max-P
 lanck Institute for Mathematics in the Sciences)
LOCATION:MR12
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