Analysis and Probability Seminar

In this talk we will introduce a particular model of a random walk in a dynamic random environment. Assign to each lattice point of Z^d a Poissonian number of particles and let each of them evolve independently as simple random walks. This constitutes our dynamic environment. On top of this environment we consider a random walk whose jump transition depends on whether there are particles present at its location or not. This is the random walk on random walks model. Previous studies have concluded that this model on Z^d has a diffusive scaling when the density of particles is sufficiently low or sufficiently high. We will argue that this holds for all densities for the model on Z^d with d\geq 5. Our proof of this rely on a novel domination result for the dynamic environment that, when combined with coupling arguments and standard random walk estimates, yield uniform mixing bounds for the so-called local environment process.

Based on joint work in progress with Florian Völlering (University of Leipzig)