Proves that sum of Steinhaus random multiplicative function over A converges to CN(0,1) only if |A|=o(N), with sharpness for most sets of density ρ where (1-ρ)^{-1}=o((log log N)^{1/2}).
Probability: A Graduate Course , shorttitle =
4 Pith papers cite this work. Polarity classification is still indexing.
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Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.
Low-resolution data improves high-resolution model performance when high-resolution samples are limited, via KL-divergence bounds and experiments on vision transformers and CNNs.
Resolvents of the sample covariances in the separable mixture model approximate deterministic matrices defined via solutions to a dual system of equations, without simultaneous diagonalizability assumptions.
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A parameterized family of balance indices for phylogenetic networks
Defines the H_α family of balance indices for phylogenetic networks, establishes structural properties including a grafting property, and analyzes minima, maxima, and distributions under random models such as Yule and PDA.