On a Problem of M. Kac on Laplace Distributions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911569947918336 |
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| author | Koirala, Robert |
| author_facet | Koirala, Robert |
| contents | 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 Cramér--Lévy 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04882 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Problem of M. Kac on Laplace Distributions Koirala, Robert Probability 60E10, 60E07, 60B15 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 Cramér--Lévy 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. |
| title | On a Problem of M. Kac on Laplace Distributions |
| topic | Probability 60E10, 60E07, 60B15 |
| url | https://arxiv.org/abs/2604.04882 |