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arXiv · 1304.2179

A characterization of limiting functions arising in mod-* convergence

Emmanuel Kowalski·Joseph Najnudel·Ashkan Nikeghbali
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Abstract

In this note, we characterize the limiting functions in mod-Gausssian convergence; our approach sheds a new light on the nature of mod-Gaussian convergence as well. Our results in fact more generally apply to mod-* convergence, where * stands for any family of probability distributions whose Fourier transforms do not vanish. We moreover provide new examples, including two new examples of (restricted) mod-Cauchy convergence from arithmetics related to Dedekind sums and the linking number of modular geodesics.

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Emmanuel Kowalski, Joseph Najnudel, Ashkan Nikeghbali. 2013-04-08. A characterization of limiting functions arising in mod-* convergence. https://arxiv.org/abs/1304.2179

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