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Crossing Velocities and Random Lattice Animals

Alain-Sol Sznitman
The Annals of Probability
Vol. 23, No. 3 (Jul., 1995), pp. 1006-1023
Stable URL: http://www.jstor.org/stable/2244861
Page Count: 18
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Crossing Velocities and Random Lattice Animals
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Abstract

We consider a Brownian motion in a Poissonian potential conditioned to reach a remote location. We show that for typical configurations the expectation of the time H to reach this goal grows at most linearly in the distance from the goal to the origin. In spite of the fact that H has no finite exponential moment, we derive three exponential estimates, one of which concerns the size of a natural lattice animal attached to the trajectory of the process up to the goal.

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