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Licensed Unlicensed Requires Authentication Published by De Gruyter April 14, 2010

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

  • Jean Jacod EMAIL logo , Emmanuel Kowalski and Ashkan Nikeghbali
From the journal Forum Mathematicum


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.

Received: 2008-07-30
Revised: 2009-11-02
Published Online: 2010-04-14
Published in Print: 2011-July

© de Gruyter 2011

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