Laurent Saloff-Coste

Random walks or diffusions with Dirichlet boundary condition (killing at the boundary) admit a Perron-Frobenius eigenfunction (the unique positive normalized eigenfunction when the domain is bounded). Starting with gambler's ruin problems, we discuss...

The "doubling property" refers to the property (of a metric measure space) that max{Vol(B(x,2r))/Vol(B(x,r)): r>0} is bounded. We consider the following question: do we have good control of the doubling property for left-invariant geometries on a...

We describe detailed two-sided inequalities for the three-player ruin problem and related estimates for killed random walks in inner-uniform finite subset of grids and other graphs. The key is the simultaneous use of the appropriate Doob transform...