Victor Vargas

activity

20152024

most citedEquilibrium states and zero temperature limit on topologically transitive countable Markov shifts

13 citations · 34 across the 12 of their papers we have counts for

collaborators

13 papers

math.DS2024

Directional derivatives and the central limit theorem on compact general one-dimensional lattices

Artur O. Lopes, Victor Vargas

We will show the central limit theorem for the general one-dimensional lattice where the space of symbols is a compact metric space. We consider the CLT for Lipschitz-Gibbs probabi…

math.DS2023

A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts

Victor Vargas

Consider a topologically transitive unilateral countable Markov shift $Σ$ , a locally constant potential $ϕ : Σ \to R$ satisfying suitable conditions, and assume that $μ_{t}$ i…

math.DS2023

Grand-canonical Thermodynamic Formalism via IFS: volume, temperature, gas pressure and grand-canonical topological pressure

A. O. Lopes, E. R. Oliveira, W. de S. Pedra +1

We consider here a dynamic model for a gas in which a variable number of particles $N \in N_{0} := N \cup {0}$ can be located at a site. This point of view leads…

math-ph2023

Noncommutative integration, quantum mechanics, Tannaka's theorem for compact groupoids and examples

Artur O. Lopes, Marcos Sebastian, Victor Vargas

We consider topological groupoids in finite and also in a compact settings. In the initial sections, we introduce definitions of typical observables and we studied them in the cont…

math.DS2022★ 1 cited

Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with markovian structure

Victor Vargas

Let $M$ be a compact metric space and $X = M^{N}$ , we consider a set of admissible sequences $X_{A, I} \subset X$ determined by a continuous admissibility function $A : M…

math.DS2022★ 2 cited

Existence of the zero temperature limit of equilibrium states on topologically transitive countable Markov shifts

Elmer R. Beltrán, Jorge Littin, Cesar Maldonado +1

Consider a topologically transitive countable Markov shift $Σ$ and a summable Markov potential $ϕ$ with finite Gurevich pressure and $Var_{1} (ϕ) < \infty$ . We prove existenc…

math.DS2021★ 3 cited

Entropy, pressure, ground states and calibrated sub-actions for linear dynamics

Artur O. Lopes, Victor Vargas

Denote by $X$ a Banach space and by $T : X \to X$ a bounded linear operator with non-trivial kernel satisfying suitable conditions. We consider the concepts of entropy - for $T$ -in…

math.DS2021★ 1 cited

On involution kernels and large deviations principles on $β$ -shifts

Victor Vargas

Consider $β > 1$ and $⌊ β ⌋$ its integer part. It is widely known that any real number $α \in [0, \frac{⌊ β ⌋}{β - 1}]$ can be represented in base $β$ …

math.DS2020★ 1 cited

Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with markovian structure

Rafael Rigão Souza, Victor Vargas

Consider a compact metric space $(M, d_{M})$ and $X = M^{N}$ . We prove a Ruelle's Perron Frobenius Theorem for a class of compact subshifts with Markovian structure introduc…

math.DS2019★ 3 cited

Invariant probabilities for discrete time Linear Dynamics via Thermodynamic Formalism

Artur O. Lopes, Ali Messaoudi, M. Stadlbauer +1

We show the existence of invariant ergodic $σ$ -additive probability measures with full support on $X$ for a class of linear operators $L : X \to X$ , where $L$ is a weighted shift op…

math.DS2019★ 4 cited

The Ruelle operator for symmetric $β$ -shifts

Artur O. Lopes, Victor Vargas

Consider $m \in N$ and $β \in (1, m + 1]$ . Assume that $a \in R$ can be represented in base $β$ using a development in series $a = \sum_{n = 1}^{\infty} x (n) β^{- n}$ …

math.DS2019★ 6 cited

Gibbs States and Gibbsian Specifications on the space $R^{N}$

Artur O. Lopes, Victor Vargas

We are interested in the study of Gibbs and equilbrium probabilities on the lattice $R^{N}$ . Consider the unilateral full-shift defined on the non-compact set $\m…

math.DS2015★ 13 cited

Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts

Ricardo Freire, Victor Vargas

Consider a topologically transitive countable Markov shift and, let $f$ be a summable potential with bounded variation and finite Gurevic pressure. We prove that there exists an eq…

Directional derivatives and the central limit theorem on compact general one-dimensional lattices

A Large deviations principle at zero temperature for stationary Markov equilibrium states on countable Markov shifts

Grand-canonical Thermodynamic Formalism via IFS: volume, temperature, gas pressure and grand-canonical topological pressure

Noncommutative integration, quantum mechanics, Tannaka's theorem for compact groupoids and examples

Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with markovian structure

Existence of the zero temperature limit of equilibrium states on topologically transitive countable Markov shifts

Entropy, pressure, ground states and calibrated sub-actions for linear dynamics

On involution kernels and large deviations principles on β-shifts

Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with markovian structure

Invariant probabilities for discrete time Linear Dynamics via Thermodynamic Formalism

The Ruelle operator for symmetric β-shifts

Gibbs States and Gibbsian Specifications on the space RN

Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts

On involution kernels and large deviations principles on $β$ -shifts

The Ruelle operator for symmetric $β$ -shifts

Gibbs States and Gibbsian Specifications on the space $R^{N}$