Under minimal Kahane-Peyriere integrability, dyadic Mandelbrot cascades satisfy dim_F(mu) = dim_E(mu) = dim_2(mu) = D_E(X) almost surely on non-extinction, with explicit sup formulas for scalar and circle cases.
[HeK71] Raphael Hø egh Krohn
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Imaginary Gaussian multiplicative chaos has Fourier dimension 1 - β² almost surely in the subcritical regime β ∈ (0,1).
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Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability
Under minimal Kahane-Peyriere integrability, dyadic Mandelbrot cascades satisfy dim_F(mu) = dim_E(mu) = dim_2(mu) = D_E(X) almost surely on non-extinction, with explicit sup formulas for scalar and circle cases.
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Fourier dimension of imaginary Gaussian multiplicative chaos
Imaginary Gaussian multiplicative chaos has Fourier dimension 1 - β² almost surely in the subcritical regime β ∈ (0,1).