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<p>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.</p>

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Harmonic analysis of Gaussian multiplicative chaos on the circle

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Christophe Garban,
  • Vincent Vargas

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.