Random walk on the simple symmetric exclusion process

With Daniel Kious (Bath)

Random walk on the simple symmetric exclusion process

In a joint work with Marcelo R. Hilário and Augusto Teixeira, we in- vestigate 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 ρ in [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− and ρ+ 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.

Add to your calendar or Include in your list

How can mathematics help us to understand the behaviour of ants? Read more about the fanscinating work being carri… https://t.co/iCODvvxqE6 View on Twitter