# Littlewood-Offord Inequalities for Random Variables

@article{Leader1994LittlewoodOffordIF,
title={Littlewood-Offord Inequalities for Random Variables},
journal={SIAM J. Discrete Math.},
year={1994},
volume={7},
pages={90-101}
}
The concentration of a real-valued random variable $X$ is $$c(X)=\sup_{t \in {\Bbb R}} {\bf P} (t < X < t+1).$$ Given bounds on the concentrations of n independent random variables, how large can the concentration of their sum be? The main aim of this paper is to give a best possible upper bound for the concentration of the sum of $n$ independent random variables, each of concentration at most $1/k$, where $k$ is an integer. Other bounds on the concentration are also discussed, as well as… CONTINUE READING

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