Mod-Poisson convergence in probability and number theory
International Mathematics Research Notices(2010)
摘要
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 anal...
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关键词
random permutations,katz-sarnak philosophy. 1 although this new paper is largely self-contained,it is likely to be most useful for,erdýos-kac theorem,. poisson distribution,distribution of val- ues of l-functions,poisson convergence
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