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arXiv · 1610.09731

Trapping planar Brownian motion in a non circular trap

Jeffrey Schenker
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Abstract

Brownian motion in the plane in the presence of a "trap" at which motion is stopped is studied. If the trap $T$ is a connected compact set, it is shown that the probability for planar Brownian motion to hit this set before a given time $t$ is well approximated even at short times by the probability that Brownian motion hits a disk of radius $r_T$ equal to the conformal radius of the trap $T$.

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Jeffrey Schenker. 2016-10-30. Trapping planar Brownian motion in a non circular trap. https://doi.org/10.30757/alea.v15-10

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