BROWNIAN MOTION AND THERMAL CAPACITY

Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W (E) boolean AND F, where E subset of (0, infinity) and F subset of R-d 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 x F, where E x F is viewed as a subspace of space time.