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Description of random fields by means of one-point finite-conditional distributions

  • A. S. DalalyanEmail author
  • B. S. Nahapetian
Statistical Physics
  • 51 Downloads

Abstract

The aim of this note is to investigate the relationship between strictly positive random fields on a lattice ℤ ν and the conditional probability measures at one point given the values on a finite subset of the lattice ℤ ν . We exhibit necessary and sufficient conditions for a one-point finite-conditional system to correspond to a unique strictly positive probability measure. It is noteworthy that the construction of the aforementioned probability measure is done explicitly by some simple procedure. Finally, we introduce a condition on the one-point finite conditional system that is sufficient for ensuring the mixing of the underlying random field.

Keywords

Random field one-point conditional distribution mixing properties 

MSC2010 numbers

82C70 60G60 

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Copyright information

© Allerton Press, Inc. 2011

Authors and Affiliations

  1. 1.Ecole des Ponts ParisTechUniversité Paris-EstParisFrance
  2. 2.Institute of MathematicsNational Academy of Sciences of ArmeniaYerevanArmenia

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