Φ-moment inequalities for independent and freely independent random variables

Concentration and moment inequalities for polynomials of independent random variables

In this work we design a general method for proving moment inequalities for polynomials of independent random variables. Our method works for a wide range of random variables including Gaussian, Boolean, exponential, Poisson and many others. We apply our method to derive general concentration inequalities for polynomials of independent random variables. We show that our method implies concentra...

Moment inequalities for functions of independent random variables

A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [7], and is based on a generalized tensorization inequality due to Lata la and Oleszkiewicz [25]. The new inequalities prove to be a versatile tool in a wide range o...

Moment inequalities for sums of certain independent symmetric random variables

This paper gives upper and lower bounds for moments of sums of independent random variables (Xk) which satisfy the condition that P (|X|k ≥ t) = exp(−Nk(t)), where Nk are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which N(t) = |t| for some fixed 0 < r ≤ 1. This complements work of Glus...

Addition of Freely Independent Random Variables

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

Polynomials of independent random variables arise in a variety of fields such as Machine Learning, Analysis of Boolean Functions, Additive Combinatorics, Random Graphs Theory, Stochastic Partial Differential Equations etc. They naturally model the expected value of objective function (or lefthand side of constraints) for randomized rounding algorithms for non-linear optimization problems where ...