Localization for a Random Walk in Slowly Decreasing Random Potential

A Random Walk with Exponential Travel Times

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Large Deviations for Random Walk in Random

Localization of the maximal entropy random walk.

We define a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk loca...

Random Walk in Random Groups

This paper compiles basic components of the construction of random groups and of the proof of their properties announced in [G10]. Justification of each step, as well as the interrelation between them, is straightforward by available techniques specific to each step. On the other hand, there are several ingredients that cannot be truly appreciated without extending the present framework. We sha...