Electronic Communications in Probability

A characterization of limiting functions arising in Mod-* convergence

Emmanuel Kowalski, Joseph Najnudel, and Ashkan Nikeghbali

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 79, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465321006

Digital Object Identifier
doi:10.1214/ECP.v20-4381

Mathematical Reviews number (MathSciNet)
MR3434196

Zentralblatt MATH identifier
1328.60010

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization 60E05: Distributions: general theory 11F20: Dedekind eta function, Dedekind sums

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Kowalski, Emmanuel; Najnudel, Joseph; Nikeghbali, Ashkan. A characterization of limiting functions arising in Mod-* convergence. Electron. Commun. Probab. 20 (2015), paper no. 79, 11 pp. doi:10.1214/ECP.v20-4381. https://projecteuclid.org/euclid.ecp/1465321006


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References

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