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arXiv · 1811.00353

Hanson-Wright inequality in Banach spaces

Radosław Adamczak·Rafał Latała·Rafał Meller
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Abstract

We discuss two-sided bounds for moments and tails of quadratic forms in Gaussian random variables with values in Banach spaces. We state a natural conjecture and show that it holds up to additional logarithmic factors. Moreover in a certain class of Banach spaces (including $L_r$-spaces) these logarithmic factors may be eliminated. As a corollary we derive upper bounds for tails and moments of quadratic forms in subgaussian random variables, which extend the Hanson-Wright inequality.

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BibTeXRIS

Radosław Adamczak, Rafał Latała, Rafał Meller. 2018-11-01. Hanson-Wright inequality in Banach spaces. https://doi.org/10.1214/19-aihp1041

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