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

Jorge Littin and Servet Martínez

Stochastic Processes and their Applications, 2010, vol. 120, issue 12, 2432-2446

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].

Keywords: Nearest; neighbors; R-positivity; Gibbs; measures; Geometric; ergodicity (search for similar items in EconPapers)
Date: 2010
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