Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails

Abstract

We present two-sided estimates of moments and tails of polynomial chaoses of order at most three generated by independent symmetric random variables with log-concave tails as well as for chaoses of arbitrary order generated by independent symmetric exponential variables. The estimates involve only deterministic quantities and are optimal up to constants depending only on the order of the chaos variable.

References in corpus (2)

• Estimates of moments and tails of Gaussian chaoses
• Moment inequalities for U-statistics

Cited by in corpus (7)

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• A note on concentration for polynomials in the Ising model
• Marchenko-Pastur law with relaxed independence conditions
• Moments of Gaussian chaoses in Banach spaces
• Two-sided moment estimates for a class of nonnegative chaoses
• Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order