Russell Impagliazzo, Valentine Kabanets

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 ...
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Chris Beck, Russell Impagliazzo, Shachar Lovett

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 >>>