Geometric Perspective on Concentration Phenomena in Frame Theory
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909014604906496 |
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| author | Ballas, Samuel Karabatman, Ferhat Needham, Tom |
| author_facet | Ballas, Samuel Karabatman, Ferhat Needham, Tom |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_03867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Perspective on Concentration Phenomena in Frame Theory Ballas, Samuel Karabatman, Ferhat Needham, Tom Functional Analysis Probability 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. |
| title | Geometric Perspective on Concentration Phenomena in Frame Theory |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2605.03867 |