Estimates of moments and tails of Gaussian chaoses

By Rafal Latala. 2005

144 citations recorded by the source corpus.

We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form ∑ai1,…,idgi1⋯gid, where gi are i.i.d. ${\mathcal{N}}(0,1)$ r.v.’s. Estimates are exact up to constants depending on d only.

Subfields: Finance, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1057fd001af4f6099e6dd19b8422958c03064d95

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Citations in the corpus

Moment inequalities for U-statistics (2005, background): “We will, however, follow [9] and give an alternate definition which is equivalent, but more straightforward.”
Bernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case (2011, methodology): “The conclusion is that it is likely that there exists a yet to be discovered concentration inequality for polynomials of independent centered subgaussian random variables that dominates ours (Theorem 1.3), Hypercontractivity (Theorem 1.6) and Latala’s [13] concentration inequalities in this setting.”
Better Agnostic Clustering Via Relaxed Tensor Norms (2017, background): “It is a special case of results due to Adamczak and Wolﬀ [AW15] (see Theorem 3.3 and the ensuing discussion therein); those results in turn build on work of Latała [Lat06].”
Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order (2013, background): “As already mentioned we will present in detail only the results from [43], which are our main tool as well as motivation.”
Concentration inequalities for polynomials in α-sub-exponential random variables (2019, methodology): “The family ‖·‖J was first introduced in [22], where it was used to prove two-sided estimates for L norms of Gaussian chaos, and the definitions given above agree with the”
Hanson-Wright inequality and sub-gaussian concentration (2013, methodology): “Large deviation inequalities for polynomials of higher degree, which extend the Hanson-Wright type inequalities, have been obtained by Latala [11] and recently by Adamczak and Wolff [1].”
A note on the Hanson-Wright inequality for random vectors with dependencies (2014, methodology): “Gaussian variables it follows from estimates for general Banach space valued polynomials by Borell [8] and Arcones-Gin´e [4]. Independent proofs were also provided by Ledoux-Talagrand [21] and Latala [16, 17]. It is also well known that the general case can be reduced to the Gaussian one by comparis”
Concentration inequalities for random tensors (2019, unknown): “k op in Theorem 1.4. Remark 1.6 (Optimal dependence on d). Several existing techniques are already known to shed light on tensor concentration. Notable examples are Latala’s bound on Gaussian chaoses [17] (see [21] for an alternative proof) and its many extensions and ramiﬁcations (see e.g. [18, 4, ”
Sketching as a Tool for Numerical Linear Algebra (2014, unknown): “Lata la [73], bounds the tails of Gaussian chaoses ∑ ai1 · · · aidgi1 · · · gid .”