Brownian motion in a Poissonian potential |
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Authors: | Alain-Sol Sznitman |
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Affiliation: | (1) Department Mathematik, ETH-Zentrum, CH-8092 Zürich, Switzerland |
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Abstract: | We study here ad-dimensional Brownian motion in a random potentialV(·, ) obtained as the sum of translations of a given fixed non negative shape function at the points of a Poisson cloud of constant intensityv. We are interested in the larget behavior for typical cloud configurations, of the Brownian path in timet under the influence of the natural Feynman-Kac weight associated toV(·, ). In particular, we show that the location at timet of the process tends to be concentrated near points of suitably low local eigenvalue of –1/2+V(·,), which lie almost at distancet from the origin. Near these points one can find in the cloud a big hole or clearing of size const(logt)1/d with volume like a ball of radiusR0(d, v)(logt)1/d. |
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Keywords: | 60K40 82D30 |
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