A multidimensional analogue of the Rademacher-Gaussian tail comparison

TL;DR

This paper establishes a dimension-free tail comparison for the Euclidean norms of sums of independent random vectors uniformly distributed in centered spheres and rescaled Gaussian vectors, advancing understanding of high-dimensional probability distributions.

Contribution

It introduces a novel dimension-free tail comparison between sums of uniform sphere vectors and Gaussian vectors, extending classical tail inequalities to high dimensions.

Findings

Dimension-free tail bounds for sums of uniform sphere vectors.

Comparison with rescaled Gaussian vectors in high dimensions.

Enhanced understanding of high-dimensional tail behaviors.

Abstract

We prove a dimension-free tail comparison between the Euclidean norms of sums of independent random vectors uniformly distributed in centred Euclidean spheres and properly rescaled standard Gaussian random vectors.