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It is shown that the density of the ratio of two random variables with thesame variance and joint Gaussian density satisfies a non stationary diffusionequation. Implications of this result for kernel density estimation of thecondensed density of the generalized eigenvalues of a random matrix penciluseful for the numerical inversion of the Laplace transform is discussed.

A diffusion equation for the density of the ratio of two jointly distributed Gaussian variables and the numerical inversion of Laplace transform