• Corpus ID: 234771707

Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States

  title={Thermodynamic Formalism for Generalized Markov Shifts on Infinitely Many States},
  author={Rodrigo Bissacot and Ruy Exel and Rodrigo Frausino and Thiago Raszeja},
Given a 0-1 infinite matrix $A$ and its countable Markov shift $\Sigma_A$, one of the authors and M. Laca have introduced a kind of {\it generalized countable Markov shift} $X_A=\Sigma_A \cup Y_A$, where $Y_A$ is a special set of finite admissible words. For some of the most studied countable Markov shifts $\Sigma_A$, $X_A$ is a compactification of $\Sigma_A$, and always it is at least locally compact. We developed the thermodynamic formalism on the space $X_A$, exploring the connections with… 

Topological entropy for countable Markov shifts and Exel--Laca algebras

A bstract . Weshowthatthe(Gurevich)topologicalentropyforthecountableMarkov shiftassociatedwithaninfinitetransitionmatrix A coincides with thenon-commutative topological entropy for the Exel–Laca

Quantum Statistical Mechanics via Boundary Conditions. A Groupoid Approach to Quantum Spin Systems

We use a groupoid model for the spin algebra to introduce boundary conditions on quantum spin systems via a Poisson point process representation. We can describe KMS states of quantum systems by

Cocycles on groupoids arising from $\mathbb {N}^k$ -actions

Abstract We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space and study generalized Ruelle operators and $ C^{\ast } $ -algebras

Thermodynamic formalism for generalized countable Markov shifts

Countable Markov shifts, denoted by $\Sigma_A$ for a 0-1 infinite matrix $A$, are central objects in symbolic dynamics and ergodic theory. R. Exel and M. Laca introduced the corresponding operator