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.

Other Information: 

Probability Seminar 2006