A Thinning Analogue of de Finetti's Theorem

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dc.creatorStarr, Shannon
dc.date2004-06-18
dc.date.accessioned2026-07-07T05:09:21Z
dc.date.available2026-07-07T05:09:21Z
dc.descriptionWe consider a notion of uniform thinning for a finite sequence of random variables $(X_1,...,X_n)$ obtained by removing one random variable, uniformly at random. If a triangular array of random variables $(X_{n,k} : n \in \mathbb{N}_+, 1 \le k \le n)$ satisfies that the law of $(X_{n,1},...,X_{n,n})$ is obtained by uniformly thinning $(X_{n+1,1},...,X_{n+1,n+1})$, then we call the array thinning-invariant. We give a representation for the Choquet simplex of all thinning-invariant triangular arrays of random variables, when all random variables take values in a compact metric space (with Borel measurable distributions). We give two applications: to long-ranged, asymmetric classical spin chains, and long-ranged, asymmetric simple exclusion processes.
dc.description30 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0406364
dc.identifierhttp://arxiv.org/abs/math/0406364
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71601
dc.subjectProbability
dc.subjectMathematical Physics
dc.subject60G09; 82B20; 60J10
dc.titleA Thinning Analogue of de Finetti's Theorem
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