Event Details

The Monkey walk: a Markov process with random reinforced relocations and fading memory

In this joint work with Gerónimo Uribe Bravo, we prove and extend results from the physics literature about a random walk with random reinforced relocations. The "walker’’ evolves in Z^d or R^d according to a Markov process, except at some random jump-times, where it chooses a time uniformly at random in its past, and instantly jumps to the position it was at that random time. This walk is by definition non-Markovian, since the walker needs to remember all it’s past. We prove that, under moment conditions on the inter-jump-times, and provided that the underlying Markov process verifies a distributional limit theorem, we show a distributional limit theorem for the position of the walker at large time. The proof relies on exploiting the branching structure of this random walk with random relocations; we are able to extend the model further by allowing the memory of the walker to decay with time.