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Electronic Colloquium on Computational Complexity

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Reports tagged with concentration bounds:
TR10-072 | 19th April 2010
Russell Impagliazzo, Valentine Kabanets

Constructive Proofs of Concentration Bounds

We give a simple combinatorial proof of the Chernoff-Hoeffding concentration bound~\cite{Chernoff, Hof63}, which says that the sum of independent $\{0,1\}$-valued random variables is highly concentrated around the expected value. Unlike the standard proofs,
our proof does not use the method of higher moments, but rather uses a simple ... more >>>

TR12-042 | 17th April 2012
Chris Beck, Russell Impagliazzo, Shachar Lovett

Large Deviation Bounds for Decision Trees and Sampling Lower Bounds for AC0-circuits

There has been considerable interest lately in the complexity of distributions. Recently, Lovett and Viola (CCC 2011) showed that the statistical distance between a uniform distribution over a good code, and any distribution which can be efficiently sampled by a small bounded-depth AC0 circuit, is inverse-polynomially close to one. That ... more >>>

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