Littlewood-Offord Inequalities for Random Variables

@article{Leader1994LittlewoodOffordIF,
  title={Littlewood-Offord Inequalities for Random Variables},
  author={Imre Leader and A. J. Radcliffe},
  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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