Geometric Perspective on Concentration Phenomena in Frame Theory
Functional Analysis
2026-05-06 v1 Probability
Abstract
Parseval and equal-norm frames play a fundamental role in frame theory and signal processing. In this work, we prove non-asymptotic concentration bounds showing that random equal-norm frames are nearly Parseval with high probability, and that random Parseval frames are nearly equal-norm with high probability. Our proofs are geometric in nature, and rely on general measure concentration principles in Riemannian manifolds. As an application, we obtain a novel probabilistic upper bound for the Paulsen problem.
Cite
@article{arxiv.2605.03867,
title = {Geometric Perspective on Concentration Phenomena in Frame Theory},
author = {Samuel Ballas and Ferhat Karabatman and Tom Needham},
journal= {arXiv preprint arXiv:2605.03867},
year = {2026}
}