Continuum-sites stepping-stone models, coalescing exhcangeable partitions, and random trees

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dc.creatorDonnelly, Peter
dc.creatorEvans, Steven N.
dc.creatorFleischmann, Klaus
dc.creatorKurtz, Thomas G.
dc.creatorZhou, Xiaowen
dc.date1998-11-10
dc.date.accessioned2026-07-07T05:26:48Z
dc.date.available2026-07-07T05:26:48Z
dc.descriptionAnalogues of stepping--stone models are considered where the site--space is continuous, the migration process is a general Markov process, and the type--space is infinite. Such processes were defined in previous work of the second author by specifying a Feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing Markov processes. An alternative representation is obtained here in terms of a limit of interacting particle systems. It is shown that, under a mild condition on the migration process, the continuum--sites stepping--stone process has continuous sample paths. The case when the migration process is Brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating Brownian motion. This duality relation is also used to show that a random compact metric space that is naturally associated to an infinite family of coalescing Brownian motions on the circle has Hausdorff and packing dimension both almost surely equal to 1/2 and, moreover, this space is capacity equivalent to the middle--1/2 Cantor set (and hence also to the Brownian zero set).
dc.description41 pages
dc.identifierhttps://arxiv.org/abs/math/9811066
dc.identifierhttp://arxiv.org/abs/math/9811066
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77691
dc.subjectProbability
dc.subject60K35 (Primary) 60G57, 60J60 (Secondary)
dc.titleContinuum-sites stepping-stone models, coalescing exhcangeable partitions, and random trees
dc.typetext

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