Rademacher–Gaussian tail comparison for complex coefficients and related problems

Chasapis, Giorgos; Liu, Ruoyuan; Tkocz, Tomasz

doi:10.1090/proc/15718

Rademacher–Gaussian tail comparison for complex coefficients and related problems
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by Giorgos Chasapis, Ruoyuan Liu and Tomasz Tkocz PDF

Proc. Amer. Math. Soc. 150 (2022), 1339-1349 Request permission

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.

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