Abstract:
We analyze the concentration properties of an annealed Feynman-Kac model in distribution space. We characterize the concentration regions in terms of a variational problem involving a competition between the potential function and the mutation kernel. When the temperature parameter is evanescent with time and under appropriate hypotheses, the probability mass tends to concentrate on regions with minimal potential values. We give a precise description of these areas using non-linear semi-group contractions and large deviation techniques. We illustrate this annealed model with two physical interpretations related respectively to Markov motions in absorbing media and interacting measure valued processes.
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Received: 10 June 2002 / Accepted: 11 October 2002 Published online: 18 February 2003
Communicated by A. Kupiainen
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Moral, P., Miclo, L. Annealed Feynman-Kac Models. Commun. Math. Phys. 235, 191–214 (2003). https://doi.org/10.1007/s00220-003-0802-z
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DOI: https://doi.org/10.1007/s00220-003-0802-z