Open Access
2015 A characterization of limiting functions arising in Mod-* convergence
Emmanuel Kowalski, Joseph Najnudel, Ashkan Nikeghbali
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Electron. Commun. Probab. 20: 1-11 (2015). DOI: 10.1214/ECP.v20-4381


In this note, we characterize the limiting functions in mod-Gaussian 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. "A characterization of limiting functions arising in Mod-* convergence." Electron. Commun. Probab. 20 1 - 11, 2015.


Accepted: 31 October 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1328.60010
MathSciNet: MR3434196
Digital Object Identifier: 10.1214/ECP.v20-4381

Primary: 60B10
Secondary: 11F20 , 60B15 , 60E05

Keywords: Dedekind sums , distributions , Fourier transform , limiting functions , Mod-* convergence , modular geodesics

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