Spectral Properties of Kernel Matrices in the Flat Limit

Kernel matrices are of central importance to many applied fields. In this manuscript, we focus on spectral properties kernel in the so-called “flat limit,” which occurs when points close together relative scale kernel. We establish asymptotic expressions for determinants matrices, then leverage obtain main terms eigenvalues. Analyticity eigenprojectors yields limiting eigenvectors, strongly tied discrete orthogonal polynomials. Both smooth and finitely kernels covered, with stronger results available finite smoothness case.