• Corpus ID: 244908726

The Lanford-Ruelle theorem for actions of sofic groups

@inproceedings{Barbieri2021TheLT,
  title={The Lanford-Ruelle theorem for actions of sofic groups},
  author={Sebastiano Barbieri and Tom Meyerovitch},
  year={2021}
}
Let Γ be a sofic group, Σ be a sofic approximation sequence of Γ and X be a Γ-subshift with nonnegative sofic topological entropy with respect to Σ. Further assume that X is a shift of finite type, or more generally, that X satisfies the topological Markov property. We show that for any sufficiently regular potential f : X → R, any translation-invariant Borel probability measure on X which maximizes the measure-theoretic sofic pressure of f with respect to Σ, is a Gibbs state with respect to f… 

References

SHOWING 1-10 OF 49 REFERENCES
ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES
  • Tim Austin
  • Mathematics, Computer Science
    Forum of Mathematics, Sigma
  • 2016
TLDR
A general lower bound for the sofic entropy of a Cartesian product in terms of separate quantities for the two factor systems involved is proved, and it is proved that this lower bound is optimal in a certain sense.
Gibbs and equilibrium measures for some families of subshifts
Abstract For subshifts of finite type (SFTs), any equilibrium measure is Gibbs, as long as $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobrušin
Equivalence of relative Gibbs and relative equilibrium measures for actions of countable amenable groups
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every
Symmetric Gibbs measures
We prove that certain Gibbs measures on subshifts of finite type are nonsingular and ergodic for certain countable equivalence relations, including the orbit relation of the adic transformation (the
Measure conjugacy invariants for actions of countable sofic groups
Sofic groups were defined implicitly by Gromov in [Gr99] and explicitly by Weiss in [We00]. All residually finite groups (and hence every linear group) is sofic. The purpose of this paper is to
Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity
A dynamical system is a pair (X,G), where X is a compact metrizable space and G is a countable group acting by homeomorphisms of X . An endomorphism of (X,G) is a continuous selfmap of X which
Krieger’s finite generator theorem for actions of countable groups I
For an ergodic p.m.p. action $$G \curvearrowright (X, \mu )$$G↷(X,μ) of a countable group G, we define the Rokhlin entropy $$h^{\mathrm {Rok}}_G(X, \mu )$$hGRok(X,μ) to be the infimum of the Shannon
Krieger's finite generator theorem for actions of countable groups Ⅱ
We continue the study of Rokhlin entropy, an isomorphism invariant for probability-measure-preserving actions of countable groups introduced in Part I. In this paper we prove a non-ergodic finite
Entropy and the variational principle for actions of sofic groups
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By
Pseudo-orbit tracing and algebraic actions of countable amenable groups
Consider a countable amenable group acting by homeomorphisms on a compact metrizable space. Chung and Li asked if expansiveness and positive entropy of the action imply existence of an off-diagonal
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