Related papers: The dimension of ergodic random sequences

We introduce the concept of effective dimension for a wide class of metric spaces that are not required to have a computable measure. Effective dimension was defined by Lutz in (Lutz 2003) for Cantor space and has also been extended to…

We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…

Reimann and Slaman initiated the study of sequences that are Martin-L\"of random with respect to a continuous measure, establishing fundamental facts about NCR, the collection of sequences that are not Martin-L\"of random with respect to…

The purpose of this work is to study some monotone functionals of the heat kernel on a complete Riemannian manifold with nonnegative Ricci curvature. In particular, we show that on these manifolds, the gradient estimate of Li and Yau, the…

We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in \cite{bacry} . If M is a non degenerate multifractal measure with associated metric $\rho(x,y)=M([x,y])$ and structure function…

By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this paper, we investigate Pesin's entropy formula and SRB measures of a finitely generated random…

Let $G$ be a real Lie group, $\Lambda<G$ a lattice and $H<G$ a connected semisimple subgroup without compact factors and with finite center. We define the notion of $H$-expanding measures $\mu$ on $H$ and, applying recent work of…

The Bernoulli convolution $\nu_\lambda$ with parameter $\lambda\in(0,1)$ is the probability measure supported on $\mathbf{R}$ that is the law of the random variable $\sum\pm\lambda^n$, where the $\pm$ are independent fair coin-tosses. We…

For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…

We study approximation schemes for shift spaces over a finite alphabet using (pseudo)metrics connected to Ornstein's $\bar{d}$ metric. This leads to a class of shift spaces we call $\bar{d}$-approachable. A shift space…

Magnitude is a numerical invariant of compact metric spaces, originally inspired by category theory and now known to be related to myriad other geometric quantities. Generalizing earlier results in $\ell_1^n$ and Euclidean space, we prove…

We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

In this work we determine and discuss the entropic uncertainty measures of Shannon type for all the discrete stationary states of the multidimensional harmonic systems directly in terms of the states' hyperquantum numbers, the…

We canonically quantize $(2+1)$-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the…

Let $M$ be a $d$-dimensional closed Riemannian manifold, let $f\in\mathrm{Diff}^{1+\beta}(M)$, and denote by $m$ the Riemannian volume form of $M$. We prove that if $m\circ f^{-n}\xrightarrow[n\to\infty]{}\mu$ exponentially fast, then $\mu$…

We show that the (truth-table) Medvedev degree KLR of Kolmogorov--Loveland randomness coincides with that of Martin L\"of randomness, MLR, answering a question of Miyabe. Next, an analogue of complex packing dimension is studied which gives…

A collection of integer sequences is jointly ergodic if for every ergodic measure preserving system the multiple ergodic averages, with iterates given by this collection of sequences, converge in the mean to the product of the integrals. We…

For simplest colored branching processes we prove an analog to the McMillan theorem and calculate Hausdorff dimensions of random fractals defined in terms of the limit behavior of empirical measures generated by finite genetic lines. In…

We study the multifractal analysis of a class of equicontractive, self-similar measures of finite type, whose support is an interval. Finite type is a property weaker than the open set condition, but stronger than the weak open set…

In this short note we prove ``effective" geometric ergodicity (i.e a Perron-Frobenius theorem) for Markov chains in random mixing dynamical environment satisfying a random non-uniform version of the Doeblin condition. Effectivity here means…