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Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case

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arxiv 1109.5193 v2 pith:5D2BMQ44 submitted 2011-09-23 math.PR

classification math.PR
keywords lambdarandomvariablesindependentmultilinearabsolutebernstein-likeboolean
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abstract

We show that the probability that a multilinear polynomial $f$ of independent random variables exceeds its mean by $\lambda$ is at most $e^{-\lambda^2 / (R^q Var(f))}$ for sufficiently small $\lambda$, where $R$ is an absolute constant. This matches (up to constants in the exponent) what one would expect from the central limit theorem. Our methods handle a variety of types of random variables including Gaussian, Boolean, exponential, and Poisson. Previous work by Kim-Vu and Schudy-Sviridenko gave bounds of the same form that involved less natural parameters in place of the variance.

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Cited by 3 Pith papers

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