# Anti-concentration of random variables from zero-free regions

@inproceedings{Michelen2021AnticoncentrationOR, title={Anti-concentration of random variables from zero-free regions}, author={Marcus Michelen and Julian Sahasrabudhe}, year={2021} }

: This paper provides a connection between the concentration of a random variable and the distribution of the roots of its probability generating function. Let X be a random variable taking values in { 0 ,..., n } with P ( X = 0 ) P ( X = n ) > 0 and with probability generating function f X . We show that if all of the zeros ζ of f X satisfy | arg ( ζ ) | (cid:62) δ and R − 1 (cid:54) | ζ | (cid:54) R then Var ( X ) (cid:62) cR − 2 π / δ n , where c > 0 is a absolute constant. We show that this…

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