## Speaker:

Professor Nikolaos Zygouras

## Institution:

USC

## Time:

Tuesday, May 1, 2007 - 11:00am

## Location:

MSTB 254

Abstract : We consider a simple random walk on Z

, d > 3. We also consider

a collection of i.i.d. positive and bounded random variables ( V? (x) )x?Z d , which will

serve as a random potential. We study the annealed and quenched cost to perform

long crossings in the random potential ? + ? V? (x), where ? is positive constant

and ? > 0 small enough . These costs are measured by the Lyapounov norms We

prove the equality of the annealed and the quenched norm. We will also discuss the

relation between the Lyapounov norms and the path behavior of the random walk

in the random potential.