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

By Warren Schudy, Maxim Sviridenko. 2011

17 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Mechanics, Statistics and Probability, Pure Mathematics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

In Statistics and Probability

In Pure Mathematics

Citations in the corpus

Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order (2013, methodology): “Some recent inequalities for polynomials in subexponential random variables have been also obtained by Schudy and Sviridenko [59,60].”
Concentration inequalities for polynomials in α-sub-exponential random variables (2019, methodology): “Finally, the two works of Schudy and Sviridenko [32, 33] contain concentration inequalities for polynomials in moment bounded random variables.”