Invariant monotone coupling need not exist

• Péter Mester ^[1]
  1. [1] Indiana University
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 1, 2013, págs. 1180-1190
• Idioma: inglés
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• Resumen

  • We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that X⊂Y, although no such coupling can be invariant. Here, “invariant” means that the distribution is invariant under group multiplications.