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.
On the probability of fast exits and long stays of planar Brownian motion in simply connected domains
How round are the complementary components of planar Brownian motion?
Self-intersection local time of planar Brownian motion based on a strong approximation by random walks
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