Document Zbl 0536.60095

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An alternate proof of a correlation inequality of Harris. (English) Zbl 0536.60095

Ann. Probab. 12, 272-273 (1984).

Summary: A theorem of T. E. Harris [ibid. 5, 451-454 (1977; Zbl 0381.60072)] states that a monotone Markov process on a finite partially ordered set has positive correlations at time t (assuming positive correlations at time 0) if and only if each jump of the process is either up or down. A new proof of the sufficiency of the jump condition is presented.

Cited in 5 Documents

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60B99	Probability theory on algebraic and topological structures
60J99	Markov processes

Keywords:

correlation inequality; FKG inequality; partially ordered set

Citations:

Zbl 0381.60072

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