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In this paper we prove that $\mathbb{P}(|X| \geq \sqrt{\text{Var}(X)}) \geq 7/32$ for every finite Rademacher sum $X$, confirming a conjecture by Hitczenko and Kwapie{\'n} from 1994, and improving upon results from Burkholder, Oleszkiewicz, and Dvo\v{r}\'ak and Klein.
On a lemma of Littlewood and Offord
P. Erdös · 1945
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D. Burkholder · 1968
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H. Prawitz · 1972
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