Slow movement of random walk in random environment on a regular tree

Slow movement of random walk in random environment on a regular tree

We consider a recurrent random walk in random environment on a regular tree. Under suitable general assumptions upon the distribution of the environment, we show that the walk exhibits an unusual slow movement: the order of magnitude of the walk in the first n steps is (log n) 3 .

A subdiffusive behaviour of recurrent random walk in random environment on a regular tree

We are interested in the random walk in random environment on an infinite tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion. Our paper focuses on the almost sure asymptotic behaviours of a recurrent random walk (Xn) in random environment on a regular tree, which is closely related to Mandelbrot [13]’s multiplicative cascade. We prove, under some general assumptions up...

Random Walk in a Random Multiplieative Environment

We investigate the dynamics of a random walk in a random multiplicative medium. This results in a random, but correlated, multiplicative process for the spatial distribution of random walkers. We show how the details of these correlations determine the asymptotic properties of the walk, i.e., the central limit theorem does not apply to these multiplicative processes. We also study a periodic so...

Random Walk in Random Environment: A Counterexample?

We describe a family of random walks in random environments which have exponentially decaying correlations, nearest neighbor transition probabilities which are bounded away from 0, and yet are subdiffusive in any dimension d < o e .

Random walk on a two-dimensional random environment