Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-14T07:26:32.704Z Has data issue: false hasContentIssue false
  • English
  • Français

Probabilistic Number Theory, the GEM/Poisson-Dirichlet Distribution and the Arc-sine Law

Published online by Cambridge University Press:  01 March 1997

ULRICH MARTIN HIRTH
ULRICH MARTIN HIRTH
Affiliation:
Mathematics Department, Royal Holloway and Bedford New College, University of London, Egham Hill, Egham, Surrey TW20 0EX, UK
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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 distribution of the divisors of a random integer, due to Deshouillers, Dress and Tenenbaum [6] (see also Tenenbaum [24, II.6.2, p. 233]), – the ‘DDT theorem’ – we obtain an arc-sine law in the GEM/Poisson-Dirichlet context. In this context we also investigate the distribution of the number of components larger than ε which correspond to the number of prime factors larger than nε.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 6 , Issue 1 , March 1997, pp. 57 - 77
Copyright
1997 Cambridge University Press