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Mod-Poisson Convergence in Probability and Number Theory

Kowalski, Emmanuel ; Nikeghbali, Ashkan

In: International Mathematics Research Notices, 2010, vol. 2010, no. 18, p. 3549-3587

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    Titre
    • Mod-Poisson Convergence in Probability and Number Theory
    Auteur
    • Kowalski, Emmanuel. D-MATH, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
    • Nikeghbali, Ashkan. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • International Mathematics Research Notices, 2010, vol. 2010, no. 18, p. 3549-3587. Oxford University Press
    Autre version électronique
    Classification
    • Santé
    Identifiant OAI-PMH
    • oai:doc.rero.ch:292200
    Summary
    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 Erdős- Kac 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