Konferenzvortragsdetails

Konferenz: Symposium in Stochastics


Slowdown estimates for random walk in random environment

Vortrag von Prof. Dr. Noam Berger
Datum: 20.04.09   Zeit: 14.00 - 00.00   Raum: Y27H25

Abstract: Random walk in random environment, introduced by Solomon in 1975, is one of the most studied models for transport in irregular media. It constitutes a Markov chain on the lattice Z^d, where the transition probabilities are determined in some random manner, whose distribution is typically translation invariant and ergodic.

For a class of models of random walk in random environment, we discuss the following problem: What is the probability that the particle moves at a speed significantly slower than its predicted asymptotic speed (to be explicit, we say less than half the predicted asymptotic speed)?

As it turns out, it is easy to give a lower bound for this probability, based on the so called "naive trap analysis". In dimension greater than or equal to 4, we show an upper bound for this probability which is very close to the lower bound obtained by the naive trap analysis. This improves previously known bounds.

As a tool for obtaining the main result, we also improve certain central limit theorem estimates for this process.

No prior familiarity with random walk in random environment will be assumed. All necessary concepts will be explained during the talk.