Abstract
We investigate the longterm behavior of a random walker evolving on top of the simple symmetric exclusion process (SSEP) at equilibrium, in dimension one. 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, so that its asymptotic behavior is expected to depend on the density ρ∈ [0 , 1] of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities ρ except for at most two values ρ_{}, ρ_{+}∈ [0 , 1]. The asymptotic speed we obtain in our LLN is a monotone function of ρ. Also, ρ_{} and ρ_{+} are characterized as the two points at which the speed may jump to (or from) zero. Furthermore, for all the values of densities where the random walk experiences a nonzero speed, we can prove that it satisfies a functional central limit theorem (CLT). For the special case in which the density is 1/2 and the jump distribution on an empty site and on an occupied site are symmetric to each other, we prove a LLN with zero limiting speed. We also prove similar LLN and CLT results for a different environment, given by a family of independent simple symmetric random walks in equilibrium.
Original language  English 

Pages (fromto)  61101 
Number of pages  41 
Journal  Communications in Mathematical Physics 
Volume  379 
Early online date  26 Aug 2020 
DOIs  
Publication status  Published  31 Oct 2020 
ASJC Scopus subject areas
 Statistical and Nonlinear Physics
 Mathematical Physics
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Daniel Kious
Person: Research & Teaching