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A characterization of limiting functions arising in Mod-* convergence


Kowalski, Emmanuel; Najnudel, Joseph; Nikeghbali, Ashkan (2015). A characterization of limiting functions arising in Mod-* convergence. Electronic Communications in Probability, 20(79):online.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:October 2015
Deposited On:19 Jan 2017 07:32
Last Modified:14 Feb 2018 11:30
Publisher:Institute of Mathematical Statistics
ISSN:1083-589X
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1214/ECP.v20-4381
Related URLs:http://projecteuclid.org/euclid.ecp/1465321006 (Publisher)

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