Windings of Random Walks

Windings of Planar Random Walks and Averaged Dehn Function

We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.

A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

Random Walks on Random Graphs

The aim of this article is to discuss some of the notions and applications of random walks on finite graphs, especially as they apply to random graphs. In this section we give some basic definitions, in Section 2 we review applications of random walks in computer science, and in Section 3 we focus on walks in random graphs. Given a graphG = (V,E), let dG(v) denote the degree of vertex v for all...

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...