Resumen de Brownian motion and thermal capacity

Davar Khoshnevisan, Yimin Xiao

• Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W(E)∩F, where E⊂(0,∞) and F⊂Rd 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 d≥2, our formula can be described in terms of the Hausdorff dimension of E×F, where E×F is viewed as a subspace of space time.