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Moments of Gaussian chaoses in Banach spaces

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arxiv 2002.01790 v1 pith:BKQCINLS submitted 2020-02-05 math.PR

Rados{l}aw Adamczak , Rafa{l} Lata{l}a , Rafa{l} Meller This is my paper · ORCID
classification math.PR
keywords spacesbanachchaosesestimatesgaussianmomentstwo-sidedvalues
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We derive moment and tail estimates for Gaussian chaoses of arbitrary order with values in Banach spaces. We formulate a conjecture regarding two-sided estimates and show that it holds in a certain class of Banach spaces including L_q spaces. As a corollary we obtain two-sided bounds for moments of chaoses with values in L_q spaces based on exponential random variables.

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  1. Intrinsic Gaussian Tensor Geometry and Random Operator Spectra

    math.PR 2026-06 unverdicted novelty 6.0 of 10

    Fixed-order Hilbertian Gaussian chaos operators satisfy ||T_K^{(m)}||_{L^p S_r} ≤ C_m (p+r)^{m/2} max_S ||F_S(K)||_{S_r}, with constants independent of Hilbert dimensions and cutoff ranks.

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