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SUMMARY:Hydrodynamics for the partial exclusion process in random environm
 ent - Simone Floreani (Delft University of Technology)
DTSTART:20220225T143000Z
DTEND:20220225T150000Z
UID:TALK168020@talks.cam.ac.uk
DESCRIPTION:In this talk\, I present a partial exclusion process in random
  environment\, a system of random walks where the random environment is ob
 tained by assigning a maximal occupancy to each site of the Euclidean latt
 ice. This maximal occupancy is allowed to randomly vary among sites\, and 
 partial exclusion occurs. Under the assumption of ergodicity under transla
 tion and uniform ellipticity of the environment\, we prove that the quench
 ed hydrodynamic limit is a heat equation with a homogenized diffusion matr
 ix. To this purpose\, we exploit the stochastic self-duality property to t
 ransfer a homogenization result concerning random walks in the same enviro
 nment with arbitrary starting points&nbsp\;to the particle system.&nbsp\;T
 he first part of the talk is based on a joint work with Frank Redig (TU De
 lft) and Federico Sau (IST Austria).\nFinally\, I will discuss some recent
  progresses in the understanding of what happens when removing the uniform
  ellipticity assumption. After recalling some results on the Bouchaud&rsqu
 o\;s trap model\, I will show that\, when assuming that the maximal occupa
 ncies are heavy tailed and i.i.d.\, the hydrodynamic limit is the fraction
 al-kinetics equation. The second part of the talk is based on an ongoing p
 roject with Alberto Chiarini (University of Padova) and Frank Redig (TU De
 lft).\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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