The largest support to escape chaos in random multiplicative functions

Short summary

A new result shows that for a random multiplicative function f(n), the convergence to a complex normal distribution requires the size of a subset A to be significantly smaller than N (specifically, |A| = o(N)). This condition is proven to be sharp, as a Gaussian limit holds for sets with density ρ where (1-ρ)^-1 = o((log log N)^1/2).

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