R -positivity and the existence of zero-temperature limits of Gibbs measures on nearest-neighbor matrices
Abstract
We study the -positivity and the existence of zero-temperature limits for a sequence of infinite-volume Gibbs measures at inverse temperature associated to a family of nearest-neighbor matrices reflected at the origin. We use a probabilistic approach based on the continued fraction theory previously introduced in Ferrari and Martinez (1993) and sharpened in Littin and Martinez (2010). Some necessary and sufficient conditions are provided to ensure (i) the existence of a unique infinite-volume Gibbs measure for large but finite values of , and (ii) the existence of weak limits as . Some application examples are revised to put in context the main results of this work.
Más información
Título según WOS: | ID WOS:001071506000001 Not found in local WOS DB |
Título según SCOPUS: | ID SCOPUS_ID:85173695899 Not found in local SCOPUS DB |
Título de la Revista: | JOURNAL OF APPLIED PROBABILITY |
Editorial: | CAMBRIDGE UNIV PRESS |
Fecha de publicación: | 2023 |
DOI: |
10.1017/JPR.2023.59 |
Notas: | ISI, SCOPUS |