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 Theore
We consider powers of the absolute value of the characteristic polynomial of Haar distributed random...
For an N×N random unitary matrix U_N, we consider the random field defined by counting the number of...
Abstract A completely elementary and self-contained proof of convergence of Gaussian multiplicative ...
Building on earlier work introducing the notion of "mod-Gaussian” convergence of sequences of random...
Building on earlier work introducing the notion of “mod-Gaussian” convergence of sequences of random...
Building on earlier work introducing the notion of “mod-Gaussian ” convergence of sequences of rando...
In this note, we characterize the limiting functions in mod-Gausssian convergence; our approach shed...
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many appli...
In this paper we complete our understanding of the role played by the limiting (or residue) function...
In this paper we complete our understanding of the role played by the limiting (or residue) function...
We prove that if omega is uniformly distributed on [0, 1], then as T -> infinity, t bar right arrow ...
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $${\mathrm{Im }}\log...
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $${\mathrm{Im }}\log...
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $${\mathrm{Im }}\log...
The canonical way to establish the central limit theorem for i.i.d. random variables is to use chara...
We consider powers of the absolute value of the characteristic polynomial of Haar distributed random...
For an N×N random unitary matrix U_N, we consider the random field defined by counting the number of...
Abstract A completely elementary and self-contained proof of convergence of Gaussian multiplicative ...
Building on earlier work introducing the notion of "mod-Gaussian” convergence of sequences of random...
Building on earlier work introducing the notion of “mod-Gaussian” convergence of sequences of random...
Building on earlier work introducing the notion of “mod-Gaussian ” convergence of sequences of rando...
In this note, we characterize the limiting functions in mod-Gausssian convergence; our approach shed...
Using Fourier analysis, we study local limit theorems in weak-convergence problems. Among many appli...
In this paper we complete our understanding of the role played by the limiting (or residue) function...
In this paper we complete our understanding of the role played by the limiting (or residue) function...
We prove that if omega is uniformly distributed on [0, 1], then as T -> infinity, t bar right arrow ...
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $${\mathrm{Im }}\log...
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $${\mathrm{Im }}\log...
We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $${\mathrm{Im }}\log...
The canonical way to establish the central limit theorem for i.i.d. random variables is to use chara...
We consider powers of the absolute value of the characteristic polynomial of Haar distributed random...
For an N×N random unitary matrix U_N, we consider the random field defined by counting the number of...
Abstract A completely elementary and self-contained proof of convergence of Gaussian multiplicative ...
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