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SUMMARY:Random walk on the simple symmetric exclusion process - Daniel Kio
 us (Bath)
DTSTART:20200310T140000Z
DTEND:20200310T150000Z
UID:TALK138106@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In a joint work with Marcelo R. Hilário and Augusto Teixeira\
 , we in- vestigate the long-term behavior of a random walker evolving on t
 op of the simple symmetric exclusion process (SSEP) at equilibrium. At eac
 h jump\, the random walker is subject to a drift that depends on whether i
 t is sitting on top of a particle or a hole. The asymptotic behavior is ex
 pected to depend on the density ρ in [0\, 1] of the underlying SSEP.\nOur
  first result is a law of large numbers (LLN) for the random walker for al
 l densities ρ except for at most two values ρ− and ρ+ in [0\, 1]\, wh
 ere the speed (as a function fo the density) possibly jumps from\, or to\,
  0.\nSecond\, we prove that\, for any density corresponding to a non-zero 
 speed regime\, the fluctuations are diffusive and a Central Limit Theorem 
 holds.\nOur main results extend to environments given by a family of indep
 endent simple symmetric random walks in equilibrium.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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