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Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC

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arxiv 2411.13923 v3 pith:THRWAWKG submitted 2024-11-21 math.PR math-phmath.DSmath.FAmath.MP

Zhaofeng Lin , Yanqi Qiu , Mingjie Tan This is my paper · ORCID
classification math.PRmath-phmath.DSmath.FAmath.MP
keywords chaosconjecturedimensionsfouriergarban-vargasmultiplicativeproofanalysis
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In this paper, we establish the exact Fourier dimensions of all standard sub-critical Gaussian multiplicative chaos on the unit interval, thereby confirming the Garban-Vargas conjecture. The proof relies on a significant improvement of the vector-valued martingale method, initially developed by Chen-Han-Qiu-Wang in the studies of the Fourier dimensions of Mandelbrot cascade random measures.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus

    math.PR 2025-07 conditional novelty 8.0 of 10

    For a specially constructed log-correlated field on T^d, the GMC measure almost surely has Fourier dimension d-γ^2 when γ<√(2d)/2 and (√(2d)-γ)^2 when √(2d)/2<=γ<√(2d), for all d>=1.

  2. Microcanonical cascades and random homeomorphisms

    math.PR 2025-05 conditional novelty 8.0 of 10

    Almost surely, the Fourier dimension of a Mandelbrot microcanonical cascade measure equals log_2(1/(E[W0^2]+E[W1^2])), settling the Mandelbrot-Kahane problem for this class.

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