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Probabilistic Number Theory, the GEM/Poisson-Dirichlet Distribution and the Arc-sine Law
The prime factorization of a random integer has a GEM/Poisson-Dirichlet distribution as transparently proved by Donnelly and Grimmett [8]. By similarity to the arc-sine law for the mean distributionExpand
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A Poisson approximation for the Dirichlet law, the Ewens sampling formula and the Griffiths-Engen-McCloskey law by the Stein-Chen coupling method
We consider the random number of (Griffiths-Engen-McCloskey (GEM))-(Poisson-Dirichlet) components which are greater than e. In two alternative and similar ways, letting Dirichlet laws and EwensExpand
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From GEM back to Dirichlet via Hoppe's Urn
In generalisation of the beta law obtained under the GEM/Poisson–Dirichlet distribution in Hirth [12] we undertake here an analogous construction which results in the Dirichlet law. Our proof makesExpand
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