R-positivity of matrices and Hamiltonians on nearest neighbors trajectories

Details R-positivity of matrices and Hamiltonians on nearest neighbors trajectories R-positivity of matrices and Hamiltonians on nearest neighbors trajectories

2010-01-15

arxiv.org/abs/1001.2782v1

Mathematics

Probability

Scientific paper

We revisit the $R-$positivity of nearest neighbors matrices on ${\ZZ_+}$ and the Gibbs measures on the set of nearest neighbors trajectories on ${\ZZ_+}$ whose Hamiltonians award either visits to sites a or visits to edges. We give conditions that guarantee the $R-$positivity or equivalently the existence of the infinite volume Gibbs measure, and we show geometrical recurrence of the associated Markov chain. In this work we generalize and sharpen results obtained in [3] and [6].

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