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The comparison methodology is powerful because of the vast arsenal of tools for treating Gaussian random matrices. As applications, the paper improves on existing eigenvalue bounds for random matrices arising in spectral graph theory, quantum information theory, high-dimensional statistics, and numerical linear algebra. In particular, these techniques deliver the first complete proof that a sparse random dimension reduction map has the injectivity properties conjectured by Nelson & Nguyen in 2013.
From: Joel Tropp [view email]
[v1]
Wed, 4 Mar 2026 18:30:04 UTC (121 KB)
[v2]
Sat, 14 Mar 2026 18:12:03 UTC (117 KB)
[v3]
Sun, 5 Jul 2026 00:09:16 UTC (164 KB)
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