Random Graphs' Robustness in Random Environment

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.

Trade-Offs between Density and Robustness in Random Interconnection Graphs

Graphs are models of communication networks. This paper applies combinatorial and symbolic-analytic techniques in order to characterize the interplay between two parameters of a random graph: its density (the number of edges in the graph) and its robustness to link failures, where robustness here means multiple connectivity by short disjoint paths. A triple (G, s, t), where G is a graph and s, ...

Random Trees in Random Graphs

We show that a random labeled n-vertex graph almost surely contains isomorphic copies of almost all labeled n-vertex trees, in two senses. In the first sense, the probability of each edge occurring in the graph diminishes as n increases, and the set of trees referred to as "almost all" depends on the random graph. In the other sense, the probability of an edge occurring is fixed, and the releva...

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...