An Equivalence Principle for the Spectrum of Random Inner-Product Kernel Matrices. (arXiv:2205.06308v1 [math.PR])

We consider random matrices whose entries are obtained by applying a
(nonlinear) kernel function to the pairwise inner products between $n$
independent data vectors drawn uniformly from the unit sphere in
$\mathbb{R}^d$. Our study of this model is motivated by problems in machine
learning, statistics, and signal processing, where such inner-product kernel
random matrices and their spectral properties play important roles. Under mild
conditions on the kernel function, we establish the weak-limit of the empirical
spectral distribution of these matrices …

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