A Thinning Analogue of de Finetti's Theorem
msra(2004)
摘要
We 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.
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关键词
asymmetric exclusion processes.,de finetti's theorem,classical spin systems,exchangeability,satisfiability,random variable,compact metric space,borel measure
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