Random matrix approximation of spectra of integral operators

~H n, obtained by deleting its diagonal. It is proved that the l 2 distance between the ordered spectrum of Hn and the ordered spectrum of H tends to zero a.s. if and only if H is Hilbert‐Schmidt. Rates of convergence and distributional limit theorems for the difference between the ordered spectra of the operators Hn (or ~ H n) and H are also obtained under somewhat stronger conditions. These results apply in particular to the kernels of certain functions Ha j(L) of partial differential operators L (heat kernels, Green functions). This paper is dedicated to Richard M. Dudley on his sixtieth birthday.

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