Regenerative Composition Structures

Simple item page
dc.creatorGnedin, Alexander
dc.creatorPitman, Jim
dc.date2003-07-22
dc.date2004-07-26
dc.date.accessioned2026-07-07T04:59:51Z
dc.date.available2026-07-07T04:59:51Z
dc.descriptionA new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random set. Examples are composition structures derived from residual allocation models, including one associated with the Ewens sampling formula, and composition structures derived from the zero set of a Brownian motion or Bessel process. We provide characterisation results and formulas relating the distribution of the regenerative composition to the L{é}vy parameters of a subordinator whose range is the corresponding regenerative set. In particular, the only reversible regenerative composition structures are those associated with the interval partition of $[0,1]$ generated by excursions of a standard Bessel bridge of dimension $2 - 2 α$ for some $α\in [0,1]$.
dc.identifierhttps://arxiv.org/abs/math/0307307
dc.identifierhttp://arxiv.org/abs/math/0307307
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68153
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60G09 (Primary) 60J65, 60G51, 60E07, 05A18 (Secondary)
dc.titleRegenerative Composition Structures
dc.typetext

Files

Collections

arXiv