ESF Scientific Programme: Random Dynamics in Spatially Extended Systems (RDSES) 2002-2006

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A key large deviation principle for interacting stochastic systems

In this paper we describe two large deviation principles for the empirical process of words cut out from a random sequence of letters according to a random renewal process: one where the letters are frozen ('quenched') and one where the letters are not frozen ('annealed'). We apply these large deviation principles to five classes of interacting stochastic systems: interacting diffusions, coupled branching processes, and three examples of a polymer chain in a random environment. In particular, we show how these large deviation principles can be used to derive variational formulas for the critical curves that are associated with the phase transitions occurring in these systems, and how these variational formulas can in turn be used to prove the existence of certain intermediate phases

Berman-Konsowa principle for reversible Markov jump processes

In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability measures for random finite paths from one set to the other, the other involving a class of finite unit flows from one set to the other. The Berman-Konsowa principle complements the Dirichlet principle and the Thomson principle, and turns out to be especially useful for obtaining sharp estimates on crossover times in metastable interacting particle systems

Phase diagram for a copolymer in a micro-emulsion

Analysis and Stochastic

Metastability on the Hierarchical Lattice

Analysis and Stochastic