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Annealed Lyapounov exponents and large deviations in a Poissonian potential. I. (English) Zbl 0826.60018

Author’s abstract: We study annealed Brownian motion moving in a Poissonian cloud of killing spheres of fixed radius (hard obstacles) or in a Poissonian potential (soft obstacles). “Annealed” refers to the fact that statistical weights of interest are averaged both with respect to the path and environment measures. We construct Lyapunov exponents which for instance in the soft obstacle case measure the directional exponential decay of the environment averaged Green’s function. These exponents come naturally in the description of certain large deviation principles which govern the large time position of annealed Brownian motion in a Poissonian potential, as well as in certain large time asymptotics of the associated heat kernel.
[For part II see below].

MSC:

60F10 Large deviations

Citations:

Zbl 0826.60019
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References:

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