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Given a Lipschitz continuous potential [Formula: see text], we prove uniqueness of the Gibbs state [Formula: see text] and we show that it is a Gibbs\u2013Bowen measure and satisfies a central limit theorem. <\/jats:p>","DOI":"10.1142\/s0219493723500387","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T14:14:01Z","timestamp":1685110441000},"source":"Crossref","is-referenced-by-count":0,"title":["Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with Markovian structure"],"prefix":"10.1142","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2785-6576","authenticated-orcid":false,"given":"Victor","family":"Vargas","sequence":"first","affiliation":[{"name":"Centre for Mathematics, University of Porto, Rua do Campo Alegre 687, Porto 4169\/007, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2023,7,14]]},"reference":[{"key":"S0219493723500387BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X11004527"},{"key":"S0219493723500387BIB002","series-title":"Wiley Series in Probability and Statistics: Probability and Statistics","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316962","volume-title":"Convergenceof Probability Measures","author":"Billingsley P.","year":"1999","edition":"2"},{"key":"S0219493723500387BIB003","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s00574-014-0040-3","volume":"45","author":"da Silva E. 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