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arXiv · 2604.04882

On a Problem of M. Kac on Laplace Distributions

Robert Koirala
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Abstract

We give counterexamples to a problem of M. Kac in the Scottish Book, which asks whether a certain nonlinear operation on two characteristic functions characterizes Laplace distributions, in analogy with the Cram\'er--L\'evy theorem for Gaussian distributions. We then give an affirmative answer to a refined version of the problem. Finally, we develop a general framework for such characterization problems, construct generalized counterexamples, and pose some open questions.

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Robert Koirala. 2026-04-06. On a Problem of M. Kac on Laplace Distributions. https://arxiv.org/abs/2604.04882

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