137 citations · 408 across the 17 of their papers we have counts for
18 papers
Thermodynamic formalism for general iterated function systems with measures
Jader E. Brasil, Elismar R. Oliveira, Rafael Rigão Souza
This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators…
A characterization of the strong law of large numbers for Bernoulli sequences
Luísa Borsato, Eduardo Horta, Rafael Rigão Souza
The law of large numbers is one of the most fundamental results in Probability Theory. In the case of independent sequences, there are some known characterizations; for instance, i…
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 and . We prove a Ruelle's Perron Frobenius Theorem for a class of compact subshifts with Markovian structure introduc…
A Dynamic Model for Double Bounded Time Series With Chaotic Driven Conditional Averages
Guilherme Pumi, Taiane Schaedler Prass, Rafael Rigão Souza
In this work we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the ran…
Open quantum random walks: ergodicity, hitting times, gambler's ruin and potential theory
Carlos F. Lardizabal, Rafael R. Souza
In this work we study certain aspects of Open Quantum Random Walks (OQRWs), a class of quantum channels described by S. Attal et al. \cite{attal}. As a first objective we consider…
An Ergodic Theorem on Ergodic Transport
Joana Mohr, Rafael Rigão Souza
Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can…
Nonhomogeneous quantum Markov chains and a notion of ergodicity
Carlos F. Lardizabal, Rafael R. Souza
Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class o…
Ergodic and Thermodynamic Games
Rafael R. Souza
Let and be continuous maps defined on compact sets. Let where is -invariant…
Exclusion process with slow boundary
Rangel Baldasso, Otávio Menezes, Adriana Neumann +1
We study the hydrodynamic and the hydrostatic behavior of the Simple Symmetric Exclusion Process with \emph{slow boundary}. The term \emph{slow boundary} means that particles can b…
On a class of quantum channels, open random walks and recurrence
Carlos F. Lardizabal, Rafael R. Souza
We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combini…
Entropy, Pressure and Duality for Gibbs plans in Ergodic Transport
A. O. Lopes, J. K. Mengue, J. Mohr +1
Let be a finite set and be the Bernoulli space. Denote by the shift map acting on . For a fixed probability on with supp(), d…
Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature
Artur O. Lopes, Jairo K. Mengue, Joana Mohr +1
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space as the state space. We analyze the shift acting on $M^\ma…
The Analyticity of a Generalized Ruelle's Operator
Eduardo Antonio da Silva, Raderson Rodrigues da Silva, Rafael Rigao Souza
In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call gene…
Continuous time finite state mean field games
Diogo A. Gomes, Joana Mohr, Rafael R. Souza
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties.…
On the general one-dimensional XY Model: positive and zero temperature, selection and non-selection
A. T. Baraviera, L. M. Cioletti, A. O. Lopes +2
We consider a connected and compact manifold and we denote by the Bernoulli space of sequences represented by $$x=(... x_{-3},x_{-2},x_{-1},x_0,x_1…
Mean field limit of a continuous time finite state game
Diogo A. Gomes, Joana Mohr, Rafael R. Souza
Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large numbe…
Discrete mean field games
Diogo A. Gomes, Joana Mohr, Rafael R. Souza
In this paper we study a mean field model for discrete time, finite number of states, dynamic games. These models arise in situations that involve a very large number of agents mov…
Negative Entropy, Zero temperature and stationary Markov Chains on the interval
Artur O. Lopes, Joana Mohr, Rafael R. Souza +1
We analyze some properties of maximizing stationary Markov probabilities on the Bernoulli space , More precisely, we consider ergodic optimization for a continuou…