高斯乘性混沌的多重分形分析及其应用

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-06-14 DOI:10.1214/22-EJP893

Federico Bertacco

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引用次数: 2

摘要

设Mγ是与定义在有界域D⊂RD，D≥1上的一般对数相关高斯场相关的亚临界高斯乘性混沌测度。我们通过证明Mγ几乎可以肯定地满足多重分形形式，即

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Multifractal analysis of Gaussian multiplicative chaos and applications

Let M γ be a subcritical Gaussian multiplicative chaos measure associated with a general log-correlated Gaussian ﬁeld deﬁned on a bounded domain D ⊂ R d , d ≥ 1. We ﬁnd an explicit formula for its singularity spectrum by showing that M γ satisﬁes almost surely the multifractal formalism, i.e

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.