# Concentration of measure and generalized product of random vectors with an application to Hanson-Wright-like inequalities

arXiv: https://arxiv.org/abs/2102.08020 · HTML: https://mlsanity.com/paper/2102.08020/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 35 references that are in the map.
- First posted on arXiv 16 Feb 2021.

## Builds on (most cited first, 1 of 1)

- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)

## Built on by (most cited first, 1 of 1)

- [Influence Diagnostics in High-dimensional M-estimation: Precise Asymptotics](https://mlsanity.com/paper/2607.09250/) (2026)

## Abstract (arXiv)

Starting from concentration of measure hypotheses on m random vectors Z1,ldots, Zm, this article provides an expression of the concentration of functionals φ(Z1,ldots, Zm) where the variations of φ on each variable depend on the product of the norms (or semi-norms) of the other variables (as if φ were a product). We illustrate the importance of this result through various generalizations of the Hanson-Wright concentration inequality as well as through a study of the random matrix XDXT and its resolvent Q = (Ip - frac1nXDXT)-1, where X and D are random, which have fundamental interest in statistical machine learning applications.