R-positivity of matrices and Hamiltonians on nearest neighbors trajectories - Mathematics > ProbabilityReport as inadecuate




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Abstract: We revisit the $R-$positivity of nearest neighbors matrices on ${\ZZ +}$ andthe Gibbs measures on the set of nearest neighbors trajectories on ${\ZZ +}$whose Hamiltonians award either visits to sites a or visits to edges. We giveconditions that guarantee the $R-$positivity or equivalently the existence ofthe infinite volume Gibbs measure, and we show geometrical recurrence of theassociated Markov chain. In this work we generalize and sharpen resultsobtained in 3 and 6.



Author: Jorge Littin, Servet Martinez

Source: https://arxiv.org/







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