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Harmonic analysis of Gaussian multiplicative chaos on the circle

Christophe Garban, Vincent Vargas

7/11/23 Published in : arXiv:2311.04027

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 coefficient (for small values of the parameter underlying the GMC theory).

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Phase I & II research project(s)

  • Field Theory
  • Statistical Mechanics

Phase III direction(s)

  • Statistical Mechanics and Random Structures
  • Holography and bulk-boundary correspondence

Cyclic model for the dg dual of the BV operad

QCD Worldsheet Axion from the Bootstrap

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The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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