Sums of Steinhaus random multiplicative functions over short intervals [x, x+y] (y→∞, y=o(x)) have Gaussian limiting distributions after a normalization that is not √y when y is close to x.
arXiv preprint arXiv:2508.12956 , year =
4 Pith papers cite this work. Polarity classification is still indexing.
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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}).
For α in (1,2) the expected 2q-moment of the normalized sum of d_α(n) f(n) is bounded by (log x)^{2q(α-1)} over a power of log log x, uniformly for q up to 1/α.
Obtains unrestricted high-moment estimates and exponential tail bounds for sums of Rademacher multiplicative functions via martingales.
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A few notes on the asymptotic behavior of Rademacher random multiplicative functions
Obtains unrestricted high-moment estimates and exponential tail bounds for sums of Rademacher multiplicative functions via martingales.