Variance Based Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case

Details Variance Based Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case Variance Based Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case

2011-09-23

arxiv.org/abs/1109.5193v1

Mathematics

Probability

arXiv admin note: substantial text overlap with arXiv:1104.4997

Scientific paper

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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