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Multiple points of Brownian motion. (English) Zbl 0534.60071
Contemp. Math. 26, 387-393 (1984).
For Brownian motion in the plane, a sufficient condition for the existence of multiple points (self-intersections) in a fixed set is stated, answering a question of Lévy. The analogous problem for $${\mathbb{R}}^ 3$$ is considered; and a proof is sketched that if a compact set has positive 2-capacity, double points occur in the set, with positive probability.
For the entire collection see [Zbl 0523.00008].
##### MSC:
 60J65 Brownian motion
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