Mod-Gaussian convergence: new limit theorems in probability and number theory
By Jean Jacod, Emmanuel Kowalski, Ashkan Nikeghbali. 2008
77 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f3edd64eeaa5434937883d0031dedb0d0c56d374
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Mod-Poisson convergence in probability and number theory (2009, methodology): “. This will explain the factor Φ˜ 1 corresponding to the cycle length of random permutations. Note that shorter arguments are definitely available, using analogues of the DelangeSelberg method used in [12] (see [6, §2, Th. 1]), but this hides again the mixture of probabilistic models involved. Intere”