I-BBS recovers latent manifold dimension d and geometry from ambient distance matrices via two noise-stable integer signatures: top non-Perron multiplet multiplicity and a parameter-free shrinkage law.
On Euclidean random matrices in high dimension
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abstract
In this note, we study the n x n random Euclidean matrix whose entry (i,j) is equal to f (|| Xi - Xj ||) for some function f and the Xi's are i.i.d. isotropic vectors in Rp. In the regime where n and p both grow to infinity and are proportional, we give some sufficient conditions for the empirical distribution of the eigenvalues to converge weakly. We illustrate our result on log-concave random vectors.
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2026 1verdicts
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I-BBS: Coordinate-Free Inference of Latent Sub-Manifolds Using Random Distance Matrix Theory
I-BBS recovers latent manifold dimension d and geometry from ambient distance matrices via two noise-stable integer signatures: top non-Perron multiplet multiplicity and a parameter-free shrinkage law.