Bounds for the total variation distance between second degree polynomials in normal random variables

TL;DR

This paper establishes bounds on the total variation distance between second degree polynomials of normal variables, focusing on cases where the polynomials depend on at least three variables, to understand their distributional differences.

Contribution

It provides new bounds for total variation distance specifically for second degree polynomials in normal variables depending on three or more variables.

Findings

Derived bounds for total variation distance between quadratic forms in normal variables.

Applicable to polynomials depending on at least three variables.

Enhances understanding of distributional differences in quadratic forms.

Abstract

In this paper we study bounds for the total variation distance between two second degree polynomials in normal random variables provided that they essentially depend on at least three variables.