The total variation distance between high-dimensional Gaussians with the same mean

TL;DR

This paper establishes tight bounds on the total variation distance between high-dimensional Gaussian distributions sharing the same mean, providing precise quantitative measures of their similarity.

Contribution

It introduces bounds that are within a constant factor of each other for the total variation distance between such Gaussians, advancing understanding of their divergence.

Findings

Derived tight bounds for total variation distance

Bounds are within a constant factor of each other

Applicable to high-dimensional Gaussian comparisons

Abstract

Given two high-dimensional Gaussians with the same mean, we prove a lower and an upper bound for their total variation distance, which are within a constant factor of one another.