CRITICAL BROWNIAN SHEET DOES NOT HAVE DOUBLE POINTS

• 成果类型: Article
• 署名作者: Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulalia; Wu, Dongsheng; Xiao, Yimin
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; Universite Paris 13; University of Alabama System; University of Alabama Huntsville; Michigan State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP665
• 发表日期: 2012
• 页码: 1829-1859
• 关键词: dimension; geometry; images

摘要

We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in R-d has double points if and only if d < 4N. In particular, in the critical case where d = 4N, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning k-multiple points in the critical case k(d - 2N) = d.