Entropic Repulsion and Lack of the g-Measure Property for Dyson Models
Abstract We consider Dyson models, Ising models with slow polynomial decay, at low
temperature and show that its Gibbs measures deep in the phase transition region are not g …
temperature and show that its Gibbs measures deep in the phase transition region are not g …
Ruelle operator for continuous potentials and DLR-Gibbs measures
In this work we study the Ruelle Operator associated to a continuous potential defined on a
countable product of a compact metric space. We prove a generalization of Bowen's criterion …
countable product of a compact metric space. We prove a generalization of Bowen's criterion …
Interactions, specifications, DLR probabilities and the Ruelle operator in the one-dimensional lattice
L Cioletti, AO Lopes - arXiv preprint arXiv:1404.3232, 2014 - arxiv.org
In this paper, we describe several different meanings for the concept of Gibbs measure on
the lattice $\mathbb {N} $ in the context of finite alphabets (or state space). We compare and …
the lattice $\mathbb {N} $ in the context of finite alphabets (or state space). We compare and …
On information gain, Kullback-Leibler divergence, entropy production and the involution kernel
AO Lopes, JK Mengue - arXiv preprint arXiv:2003.02030, 2020 - arxiv.org
It is well known that in Information Theory and Machine Learning the Kullback-Leibler
divergence, which extends the concept of Shannon entropy, plays a fundamental role. Given …
divergence, which extends the concept of Shannon entropy, plays a fundamental role. Given …
Thermodynamical and spectral phase transition for local diffeomorphisms in the circle
T Bomfim, V Carneiro - Nonlinearity, 2023 - iopscience.iop.org
It is known that all uniformly expanding dynamics have no phase transition with respect to
Hölder continuous potentials. In this paper we show that given a local diffeomorphism f on …
Hölder continuous potentials. In this paper we show that given a local diffeomorphism f on …
On the dimension of the space of harmonic functions on transitive shift spaces
L Cioletti, L Melo, R Ruviaro, EA Silva - Advances in Mathematics, 2021 - Elsevier
In this paper, we show a new relation between phase transition in Statistical Mechanics and
the dimension of the space of harmonic functions (SHF) for a transfer operator. This is …
the dimension of the space of harmonic functions (SHF) for a transfer operator. This is …
Curie–Weiss type models for general spin spaces and quadratic pressure in ergodic theory
R Leplaideur, F Watbled - Journal of Statistical Physics, 2020 - Springer
We extend results on quadratic pressure and convergence of Gibbs measures from
Leplaideur and Watbled (Bull Soc Math France 147 (2): 197–219, 2019) to some general …
Leplaideur and Watbled (Bull Soc Math France 147 (2): 197–219, 2019) to some general …
The double transpose of the ruelle operator
In this paper we study the double transpose of the $ L^ 1 (X,\mathscr {B}(X),\nu) $-
extensions of the Ruelle transfer operator $\mathscr {L} _ {f} $ associated to a general real …
extensions of the Ruelle transfer operator $\mathscr {L} _ {f} $ associated to a general real …
Correlation inequalities and monotonicity properties of the Ruelle operator
L Cioletti, AO Lopes - Stochastics and Dynamics, 2019 - World Scientific
In this paper, we provide sufficient conditions for the validity of the FKG Inequality, on
Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle …
Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle …
On controlled specification and uniqueness of the equilibrium state in expansive systems
R Pavlov - Nonlinearity, 2019 - iopscience.iop.org
Abstract In Bowen (1974/75 Math. Syst. Theory 8 193–202), Bowen showed that for an
expansive system with specification and a potential with the Bowen property, the equilibrium …
expansive system with specification and a potential with the Bowen property, the equilibrium …