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.
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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.