An Isaac Newton Institute Workshop

First-Passage and Extreme Value Problems in Random Processes

Maximum of a brownian path, fluctuating interfaces and related problems

28th June 2006

Author: Comtet, A (Universite Paris 11)

Abstract

We present some functionals of the one dimensional Brownian motion which arise in various statistical physics problems: -maximal fluctuation of a growing interface -traversal time of a potential barrier -search algorithm of the maximum of a simple random walk. All these different cases involve certain functionals of the path and its maximum. We show how to compute these distributions by a path integral approach and discuss the link with probabilistic techniques based on meanders and excursions.