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Crossing Velocities and Random Lattice Animals
The Annals of Probability
Vol. 23, No. 3 (Jul., 1995), pp. 1006-1023
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2244861
Page Count: 18
You can always find the topics here!Topics: Velocity, Brownian motion, Cubes, Mathematical lattices, Mathematical theorems, Infinity, Stopping distances
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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.
The Annals of Probability © 1995 Institute of Mathematical Statistics