Random walks in I.I.D. random environment on Cayley trees

Branching random walks in random environment on Cayley graphs

We review some recent results concerning recurrence and transience for branching random walks in random environment on ddimensional lattices and on trees. We obtain some generalizations of these results for the case when the branching random walk in random environment takes place on arbitrary infinite connected Cayley graph.

Random Walks in Random Environment

Random Walks in Random Environment

My main research interest is in theoretical and applied probability mainly focusing on discrete problems arising out of combinatorics, statistical physics and computer science. In particular I am interested in random graphs, probability on tress, combinatorial optimization and statistical physics problems, recursive distributional equations, branching random walks, percolation theory, interacti...

Random walks on directed Cayley graphs

Previous authors have shown bounds on mixing time of random walks on finite undirected Cayley graphs, both with and without self-loops. We extend this to the most general case by showing that a similar bound holds for walks on all finite directed Cayley graphs. These are shown by use of two new canonical path theorems for mixing time of non-reversible Markov chains. The first result is related ...

Random walks on complex trees.

We study the properties of random walks on complex trees. We observe that the absence of loops is reflected in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and the mean topological displacement from the origin present a considerable slowing down in the tree case. Second, the mean first passage time (MFPT) display...