Related papers: Some notes on variational principle for metric mea…
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving…
Recently Bingbing Liang and Hanfeng Li computed the mean dimension and metric mean dimension for algebraic actions of amenable groups. We show how to extend their computation of metric mean dimension to the case of sofic groups, provided…
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
In this paper, we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective…
We study the metric mean dimension of $\Phi$-irregular set $I_{\Phi}(f)$ in dynamical systems with the shadowing property. In particular we prove that for dynamical systems with shadowing containing a chain recurrent class $Y$, the values…
A breakthrough result of B\'ar\'any, Hochman and Rapaport published in 2019 established that every self-affine measure on $\mathbb{R}^2$ satisfying certain mild non-degeneracy conditions has Hausdorff dimension equal to its Lyapunov…
The purpose of the present paper is to establish moderate deviation principles for a rather general class of random variables fulfilling certain bounds of the cumulants. We apply a celebrated lemma of the theory of large deviations…
Let $\mu$ be a Gibbs measure of the doubling map $T$ of the circle. For a $\mu$-generic point $x$ and a given sequence $\{r_n\} \subset \R^+$, consider the intervals $(T^nx - r_n \pmod 1, T^nx + r_n \pmod 1)$. In analogy to the classical…
Wu and Verd\'u developed a theory of almost lossless analog compression, where one imposes various regularity conditions on the compressor and the decompressor with the input signal being modelled by a (typically infinite-entropy)…
R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…
In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are…
The purpose of this paper is to generalize the variational principle, which states that the topological entropy is equal to the supremum of the measure theoretical entropies and also the minimum of the metric theoretical entropies, to…
We are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of…
We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators. As an application, we explore some consequences of our…
Moderate deviation principles for stochastic differential equations driven by a Poisson random measure (PRM) in finite and infinite dimensions are obtained. Proofs are based on a variational representation for expected values of positive…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
In this paper we introduce a topology under which the pair empirical measure of a large class of random walks satisfies a strong Large Deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and…
When using the maximin principle to solve the problem of classifying digital objects according to histograms, generated by this objects, it becomes necessary to take into account all the vertices of the polyhedron, generated by inequalities…