## Electronic Communications in Probability

### A characterization of limiting functions arising in Mod-* convergence

#### 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

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

#### References

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