Improved bandwidth approximation for trees
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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The concentration of a real-valued random variable $X$ is $$ c(X)=\sup_{t \in {\Bbb R}} {\bf P} (t $$ 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 the case of vector-valued random variables.