Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

6 Issues per year


IMPACT FACTOR 2017: 0.695
5-year IMPACT FACTOR: 0.750

CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 0.966
Source Normalized Impact per Paper (SNIP) 2017: 0.889

Mathematical Citation Quotient (MCQ) 2016: 0.75

Online
ISSN
1435-5337
See all formats and pricing
More options …
Volume 23, Issue 4

Issues

Mod-Gaussian convergence: new limit theorems in probability and number theory

Jean Jacod
  • Institut de mathématiques de Jussieu, Université Pierre et Marie Curie, et C.N.R.S. UMR 7586, 175, rue du Chevaleret, 75013 Paris, France.
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Emmanuel Kowalski / Ashkan Nikeghbali
Published Online: 2010-04-14 | DOI: https://doi.org/10.1515/form.2011.030

Abstract

We introduce a new type of convergence in probability theory, which we call “mod-Gaussian convergence”. It is directly inspired by theorems and conjectures, in random matrix theory and number theory, concerning moments of values of characteristic polynomials or zeta functions. We study this type of convergence in detail in the framework of infinitely divisible distributions, and exhibit some unconditional occurrences in number theory, in particular for families of L-functions over function fields in the Katz–Sarnak framework. A similar phenomenon of “mod-Poisson convergence” turns out to also appear in the classical Erdős–Kac Theorem.

Keywords.: Limit theorems; random matrices; characteristic polynomial; infinitely divisible distributions; zeta and L-functions; Katz–Sarnak philosophy; Erdős–Kac Theorem

About the article

Received: 2008-07-30

Revised: 2009-11-02

Published Online: 2010-04-14

Published in Print: 2011-07-01


Citation Information: Forum Mathematicum, Volume 23, Issue 4, Pages 835–873, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.030.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Martina Dal Borgo, Emma Hovhannisyan, and Alain Rouault
Annales Henri Poincaré, 2018
[3]
Rita Giuliano and Claudio Macci
Mathematics, 2018, Volume 6, Number 4, Page 49
[4]
M. Dal Borgo, E. Hovhannisyan, and A. Rouault
Journal of Statistical Physics, 2017
[5]
Dmitry Ostrovsky
Journal of Statistical Physics, 2016, Volume 164, Number 6, Page 1292
[6]
Dmitry Ostrovsky
Nonlinearity, 2016, Volume 29, Number 2, Page 426
[7]
Yacine Barhoumi-Andréani, Christopher Hughes, Joseph Najnudel, and Ashkan Nikeghbali
International Mathematics Research Notices, 2015, Page rnv060
[8]
Christophe Delaunay and Frédéric Jouhet
Advances in Mathematics, 2014, Volume 258, Page 13
[9]
Martin Wahl
Mathematische Zeitschrift, 2014, Volume 276, Number 3-4, Page 635

Comments (0)

Please log in or register to comment.
Log in