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SUMMARY:Random walk on the simple symmetric exclusion process - Daniel Kio
us (University of Bath)
DTSTART;VALUE=DATE-TIME:20220126T120000Z
DTEND;VALUE=DATE-TIME:20220126T130000Z
UID:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
DESCRIPTION:In a joint work with Marcelo R. Hilário and Augusto Teixeira\
, we investigate the long-term behavior of a random walker evolving on top
of the simple symmetric exclusion process (SSEP) at equilibrium. At each
jump\, the random walker is subject to a drift that depends on whether it
is sitting on top of a particle or a hole. The asymptotic behavior is expe
cted to depend on the density ρ in [0\, 1] of the underlying SSEP.\nOur f
irst result is a law of large numbers (LLN) for the random walker for all
densities ρ except for at most two values ρ− and ρ+ in [0\, 1]\, wher
e the speed (as a function of the density) possibly jumps from\, or to\, 0
. \nSecond\, we prove that\, for any density corresponding to a non-zero s
peed regime\, the fluctuations are diffusive and a Central Limit Theorem h
olds.\nFor the special case in which the density is 1/2 and the jump distr
ibution on an empty site and on an occupied site are symmetric to each oth
er\, we prove a LLN with zero limiting speed.\nOur main results extend to
environments given by a family of independent simple symmetric random walk
s in equilibrium.\nSpeakers:\nDaniel Kious (University of Bath)
LOCATION:Mathematical Institute (Room L3)\, Woodstock Road OX2 6GG
TZID:Europe/London
URL:https://talks.ox.ac.uk/talks/id/38d0d7bd-deb2-4b71-9b39-a771c5a53d30/
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DESCRIPTION:Talk:Random walk on the simple symmetric exclusion process - D
aniel Kious (University of Bath)
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