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.
Micro-canonical cascades and random homeomorphisms
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A single algebraic mixed-coincidence identity is proved that recovers Sanov decompositions, Chernoff information, PAC-Bayes bounds, and Renyi variational formulas as special cases while generalizing them to any number of priors.
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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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Information from coincidences
A single algebraic mixed-coincidence identity is proved that recovers Sanov decompositions, Chernoff information, PAC-Bayes bounds, and Renyi variational formulas as special cases while generalizing them to any number of priors.