Ages of Records in Random Walks

$\delta$-exceedance records and random adaptive walks

We study a modified record process where the k’th record in a series of independent and identically distributed random variables is defined recursively through the condition Yk > Yk−1 − δk−1 with a deterministic sequence δk > 0 called the handicap. For constant δk ≡ δ and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition a...

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 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 in Random Environments

Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium (for a general reference see, e.g., Hughes (1995)). However, in many practical cases the medium where the system evolves is highly irregular, due to factors such as defects, impurities, fluctuations etc. It is natural to model such irr...