Ewens sampling formulae with and without selection.

Consider the random Dirichlet partition of the interval into $n$ fragments at temperature $\theta >0.$ Using calculus for Dirichlet integrals, pre-asymptotic versions of the Ewens sampling formulae from finite Dirichlet partitions can be obtained. From these, straightforward proofs of the usual sampling formulae from random proportions with Poisson-Dirichlet PD$\left( \gamma \right) $ distribution can be supplied, while considering the Kingman limit $n\uparrow \infty $, $\theta \downarrow 0,$with $n\theta =\gamma >0$. In this manuscript, the Gibbs version of the Dirichlet partition with symmetric selection is considered. Using similar calculus for Dirichlet integrals, closed-form expressions of Ewens sampling formulae in the presence of selection are obtained; special types of Bell polynomials are shown to be involved.

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Field Value
Source ISSN: 0377-0427
Author Huillet, Thierry
Maintainer CCSD
Last Updated May 7, 2026, 10:17 (UTC)
Created May 7, 2026, 10:17 (UTC)
Identifier hal-00093093
Language en
contributor Laboratoire de Physique Théorique et Modélisation (LPTM - UMR 8089) ; Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY)
creator Huillet, Thierry
date 2007-05-07T00:00:00
harvest_object_id adf7d8dd-9dbc-457e-9b55-a975cf875c37
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-03-08T00:00:00
set_spec type:ART