English

Hanson-Wright inequality in Banach spaces

Probability 2020-10-27 v3 Functional Analysis Statistics Theory Statistics Theory

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 LrL_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.

Keywords

Cite

@article{arxiv.1811.00353,
  title  = {Hanson-Wright inequality in Banach spaces},
  author = {Radosław Adamczak and Rafał Latała and Rafał Meller},
  journal= {arXiv preprint arXiv:1811.00353},
  year   = {2020}
}

Comments

MSC classification and acknowledgement added, minor typo corrected, references updated

R2 v1 2026-06-23T05:00:31.970Z