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The level sets of iterated Brownian motion
We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4.
Brownian motion in a Brownian crack
(Institute of Mathematical Statistics, 1998-08)
Let D be the Wiener sausage of width [epsilon] around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, resp., as [epsilon] goes to 0.