Rademacher-Gaussian tail comparison for complex coefficients and related problems

TL;DR

This paper extends Rademacher-Gaussian tail comparison to complex coefficients and derives bounds on the probability of large deviations for sums of random vectors with matrix weights.

Contribution

It generalizes existing tail comparison results to complex coefficients and provides uniform bounds for weighted sums of spherical random vectors.

Findings

Extended tail comparison to complex coefficients.

Established bounds on probabilities of large deviations.

Applicable to sums of independent spherical vectors with matrix weights.

Abstract

We provide a generalisation of Pinelis' Rademacher-Gaussian tail comparison to complex coefficients. We also establish uniform bounds on the probability that the magnitude of weighted sums of independent random vectors uniform on Euclidean spheres with matrix coefficients exceeds its second moment.