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The probability that Brownian motion almost covers a line

Robin Pemantle
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Abstract

Lower and upper estimates are given for the probability that the epsilon-enlargement of planar Brownian motion to time 1 (the epsilon sausage) contains a unit line segment. The estimates imply that Brownian motion to time 1 itself contains no line segment.

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Robin Pemantle. 1997-01-23. The probability that Brownian motion almost covers a line. https://doi.org/10.1016/s0246-0203(97)80119-7

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