Seminar series
Date
Mon, 14 Jan 2008
14:45
14:45
Location
Oxford-Man Institute
Speaker
Prof. Olivier Raimond
Organisation
Universite Paris-Sud XI
This is a joint work with Bruno Schapira, and it is a work in progress.
We study recurrence and transience properties of some edge reinforced random walks on the integers: the probability to go from $x$ to $x+1$ at time $n$ is equal to $f(\alpha_n^x)$ where $\alpha_n^x=\frac{1+\sum_{k=1}^n 1_{(X_{k-1},X_k)=(x,x+1)}}{2+\sum_{k=1}^n 1_{X_{k-1}=x}}$. Depending on the shape of $f$, we give some sufficient criteria for recurrence or transience of these walks