An optimal transportation approach to the decay of correlations for non-uniformly expanding maps

BR Kloeckner - Ergodic Theory and Dynamical Systems, 2020 - cambridge.org
We consider the transfer operators of non-uniformly expanding maps for potentials of
various regularity, and show that a specific property of potentials ('flatness') implies a Ruelle …

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 …

The double transpose of the ruelle operator

L Cioletti, ACD van Enter, R Ruviaro - arXiv preprint arXiv:1710.03841, 2017 - arxiv.org
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 …

Some Probabilistic Properties of General Topological Markov Chains

EA Silva, EG Mesquita, E Matias - arXiv preprint arXiv:2310.01697, 2023 - arxiv.org
In this paper, we utilize the framework of Markov processes to attain a more probabilistic
perspective on the theory of transfer operators. In doing so, we establish a functional central …

[PDF][PDF] Some Probabilistic Properties of General Topological Markov Chains

EA Silva, EG Mesquita, E Matias - arXiv e-prints, 2023 - researchgate.net
In this paper, we utilize the framework of Markov processes to attain a more probabilistic
perspective on the theory of transfer operators. In doing so, we establish a functional central …

The Involution Kernel and the Dual Potential for Functions in the Walters' Family

LY Hataishi, AO Lopes - Qualitative Theory of Dynamical Systems, 2023 - Springer
First, we set a suitable notation. Points in {0, 1} Z-{0}={0, 1} N×{0, 1} N= Ω-× Ω+, are denoted
by (y| x)=(..., y 2, y 1| x 1, x 2,...), where (x 1, x 2,...)∈{0, 1} N, and (y 1, y 2,...)∈{0, 1} N. The …

The double transpose of the Ruelle operator

L Cioletti, A Enter, R Ruviaro - Monatshefte für Mathematik, 2023 - Springer
In this paper we study the double transpose of the L 1 (X, B (X), ν)-extensions of the Ruelle
transfer operator L f associated to a general real continuous potential f∈ C (X), where X …