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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Hydrodynamics for the partial exclusion process in
random environment - Simone Floreani (Delft Unive
rsity of Technology)
DTSTART;TZID=Europe/London:20220225T143000
DTEND;TZID=Europe/London:20220225T150000
UID:TALK168020AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/168020
DESCRIPTION:In this talk\, I present a partial exclusion proce
ss in random environment\, a system of random walk
s where the random environment is obtained by assi
gning a maximal occupancy to each site of the Eucl
idean lattice. This maximal occupancy is allowed t
o randomly vary among sites\, and partial exclusio
n occurs. Under the assumption of ergodicity under
translation and uniform ellipticity of the enviro
nment\, we prove that the quenched hydrodynamic li
mit is a heat equation with a homogenized diffusio
n matrix. To this purpose\, we exploit the stochas
tic self-duality property to transfer a homogeniza
tion result concerning random walks in the same en
vironment with arbitrary starting points \;to
the particle system. \;The first part of the t
alk is based on a joint work with Frank Redig (TU
Delft) and Federico Sau (IST Austria).\nFinally\,
I will discuss some recent progresses in the under
standing of what happens when removing the uniform
ellipticity assumption. After recalling some resu
lts on the Bouchaud&rsquo\;s trap model\, I will s
how that\, when assuming that the maximal occupanc
ies are heavy tailed and i.i.d.\, the hydrodynamic
limit is the fractional-kinetics equation. The se
cond part of the talk is based on an ongoing proje
ct with Alberto Chiarini (University of Padova) an
d Frank Redig (TU Delft).\n \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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