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R-positivity of nearest neighbor matrices and applications to Gibbs states

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  • Littin, Jorge
  • Martínez, Servet

Abstract

We revisit the R-positivity of nearest neighbor matrices on and the Gibbs measures on the set of nearest neighbor trajectories on whose Hamiltonians award either visits to sites or visits to edges. We give conditions that guarantee the R-positivity or equivalently the existence of the infinite volume Gibbs measure. Moreover, we supply necessary and sufficient conditions for the geometric ergodicity of the associated Markov chain. In this work we generalize and sharpen results obtained in [7] and [11].

Suggested Citation

  • Littin, Jorge & Martínez, Servet, 2010. "R-positivity of nearest neighbor matrices and applications to Gibbs states," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2432-2446, December.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:12:p:2432-2446
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    References listed on IDEAS

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    1. Ferrari, Pablo A. & Martínez, Servet, 1998. "Hamiltonians on random walk trajectories," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 47-68, October.
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