Mod-Poisson convergence in probability and number theory
By Emmanuel Kowalski, Ashkan Nikeghbali. 2009
58 citations recorded by the source corpus.
Building on earlier work introducing the notion of "mod-Gaussian" convergence of sequences of random variables, which arises naturally in Random Matrix Theory and number theory, we discuss the analogue notion of "mod-Poisson" convergence. We show in particular how it occurs naturally in analytic number theory in the classical Erd\H{o}s-K\'ac Theorem. In fact, this case reveals deep connections and analogies with conjectures concerning the distribution of L-functions on the critical line, which belong to the mod-Gaussian framework, and with analogues over finite fields, where it can be seen as a zero-dimensional version of the Katz-Sarnak philosophy in the large conductor limit.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f5d823f11cdc59d01cc7fed9538194d48c316632
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In Algebra and Number Theory
In Mathematical Physics
- Ashkan Nikeghbali
- Emmanuel Kowalski
- Valentin F'eray
- Jean Jacod
- P. Michel
- Mark Podolskij
- V. Todorov
- Markus Reiß
Citations in the corpus
- Mod-Gaussian convergence: new limit theorems in probability and number theory (2008, background): “u/; in [12], this phenomenon is explored in greater depth.”
- Mod-ϕ Convergence (2016, background): “Indeed it is shown in [KN10] that the structure of the limiting function appearing in the moments conjecture for the Riemann zeta function by Keating and Snaith [KS00b] is shared by other arithmetic functions and that the limiting function ψ accounts for the fact that prime numbers do not behave ind”