BROWNIAN MOTION AND THERMAL CAPACITY

• 成果类型: Article
• 署名作者: Khoshnevis, Davar; Xiao, Yimin
• 署名单位: Utah System of Higher Education; University of Utah; Michigan State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP910
• 发表日期: 2015
• 页码: 405-434
• 关键词: hausdorff; sets

摘要

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.