BASIC PROPERTIES OF CRITICAL LOGNORMAL MULTIPLICATIVE CHAOS

• 成果类型: Article
• 署名作者: Barral, Julien; Kupiainen, Antti; Nikula, Miika; Saksman, Eero; Webb, Christian
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; University of Helsinki
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP931
• 发表日期: 2015
• 页码: 2205-2249
• 关键词: random-walks; cascades; martingales; turbulence; points

摘要

We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension