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Maximum of a brownian path, fluctuating interfaces and related problems

Monday 26th June 2006 - 15:30 to 16:30
INI Seminar Room 1

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.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons