Kious, Daniel <br/><br/>
Random walk on the simple symmetric exclusion process/ 
Daniel Kious. 
 - Rio de Janeiro:  IMPA,  2021. 
 - online lecture 
<br/><br/> Lecture - online event 
<br/><br/>Abstract: 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 expected to depend on the density ? in [0, 1] of the underlying SSEP. Our first result is a law of large numbers (LLN) for the random walker for all densities ? except for at most two values ?- and ?+ in [0, 1], where the speed (as a function fo the density) possibly jumps from, or to, 0. Second, we prove that, for any density corresponding to a non-zero speed regime, the fluctuations are diffusive and a Central Limit Theorem holds. Our main results extend to environments given by a family of independent simple symmetric random walks in equilibrium . 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Matematica.
<br/><br/><label>Dewey Class. No.: </label>cs