Brownian motion and thermal capacity

• Khoshnevisan, Davar ^[1] ; Xiao, Yimin ^[2]
  1. [1] University of Utah

     University of Utah

     Estados Unidos

     
  2. [2] Michigan State University

     Michigan State University

     City of East Lansing, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 43, Nº. 1, 2015, págs. 405-434
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.