Gibbs states on the symbolic space over an infinite alphabet

By R. Mauldin, Mariusz Urba'nski. 2001

171 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d169b02f071a1e08e122919babcf4dcd07b0a8cf

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In Computational Theory and Mathematics

In Condensed Matter Physics

In Mathematical Physics

Citations in the corpus

Almost isomorphism for countable state Markov shifts (2004, background): “One motivation of our paper is recent interest in the thermodynamic formalism for countable state Markov shifts [11, 18, 23, 24, 25, 39, 49, 50, 51, 53].”
Infinite alphabet edge shift spaces via ultragraphs and their C*-algebras (2017, background): “Further development of the theory appeared in [2, 3] where Boyle, Buzzi and Gómez study almost isomorphism for countable-state Markov shifts, [6, 20, 24, 27] where thermodynamical formalism for such shifts is developed, [28] where sliding block codes are characterized, and many other papers (see [25”
STATISTICAL PROPERTIES OF ONE-DIMENSIONAL MAPS WITH CRITICAL POINTS AND SINGULARITIES (2006, background): “This is based on some recent progress on the thermodynamic formalism for abstract countable shift spaces [9, 24, 32, 43, 45], recent results on the relation between invariant measures for the system and invariant measures for the Markov tower extension [54], and the application of these results to s”
Existence of gibbs measures for countable Markov shifts (2003, methodology): “This is stronger than the big images property used in [2], and for X topologically mixing, is equivalent to the finite primitivity condition used by Mauldin and Urba´nski in [7].”
Equilibrium measures for maps with inducing schemes (2006, background): “Various versions of these results were obtained by Mauldin and Urba¶nski [ MU01 ], by Sarig [Sar99], [Sar01a], [Sar03] and by Yuri [Yur99] (see also [Aar97] and [BS03]).”
A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates (2005, methodology): “Hence, all preliminaries of [20], Corollary 2.”
Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps (2003, background): “Unfortunately, if |S| = ∞ this never happens, unless A satisfies the BIP property (see [18] and [26] for statements and definitions), so the general case cannot be treated this way.”