On the most visited sites of planar Brownian motion
نویسندگان
چکیده
Let (Bt : t ≥ 0) be a standard planar Brownian motion. Dvoretzky, Erdős and Kakutani (1958) first showed that, almost surely, there exist points x in the plane such that {t ≥ 0: Bt = x}, the set of times where the Brownian path visits x, is uncountably infinite. Modern proofs of this fact are given in Le Gall (1987) and Mörters and Peres (2010). The result naturally raises the question: How large can the sets {t ≥ 0: Bt = x} be? Kaufman’s famous dimension-doubling theorem implies that, almost surely, for all points x in the plane this set has Hausdorff dimension zero.
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