176 research outputs found
Brownian motion and thermal capacity
Let denote -dimensional Brownian motion. We find an explicit formula
for the essential supremum of Hausdorff dimension of , where
and are arbitrary nonrandom
compact sets. Our formula is related intimately to the thermal capacity of
Watson [Proc. Lond. Math. Soc. (3) 37 (1978) 342-362]. We prove also that when
, our formula can be described in terms of the Hausdorff dimension of
, where is viewed as a subspace of space time.Comment: Published in at http://dx.doi.org/10.1214/14-AOP910 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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