## Some self-interacting random walks

- Date: 11/01/2006

Mark Holmes (Eurandom)

University of British Columbia

We will discuss two different classes of self-interacting random walks.

Firstly, in joint work with Akira Sakai, we consider a simple model of

a random walk with reinforcement but with very short term spatial

memory. The simplicity of these 'Senile random walks' enables us to

prove many things such as recurrence/transience and an exact expression

for the diffusion constant. Secondly, in joint work with Remco van der

Hofstad, we derive an expansion for general self-interacting random

walks. We use the expansion to prove a central limit theorem for a

class of once reinforced random walks with non-zero drift (all

dimensions) and for excited random walk (high dimensions), when the

reinforcement and excitement parameters are sufficiently small.

Probability Seminar 2006