Harmonic analysis of Gaussian multiplicative chaos on the circle

• 成果类型: Article
• 署名作者: Garban, Christophe; Vargas, Vincent
• 署名单位: Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France; University of Geneva; University of Geneva
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01497-7
• 发表日期: 2026-08
• 页码: 1275-1297
• 关键词: coefficients

摘要

In this paper, we initiate the harmonic analysis of Gaussian multiplicative chaos (GMC) on the circle, i.e. the study of its Fourier coefficients. In particular, we show that almost surely GMC is a so-called Rajchman measure which means that its Fourier coefficients converge to 0 when the frequency goes to infinity. We supplement this result with a convergence in law result for the rescaled Fourier coefficients.