Related papers: Random noble means substitutions
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
We present a model that investigates the spontaneous emergence of randomness in equity market microstructure. The phase space analysis of our model exposes an endogenous source of fluctuation in price and volume. We formulate a control…
We derive a formula for the nonequilibrium entropy of a classical stochastic field in terms of correlation functions of this field. The formalism is then applied to define the entropy of gravitational perturbations (both gravitational waves…
We introduce and study a notion of algebraic entropy for self-maps of finite length of Noetherian local rings, and develop its properties. We show that it shares the standard properties of topological entropy. For finite self-maps we…
We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…
We provide a comprehensive numerical study of the Emergent Cyclic Inflation scenario. This is a scenario where instead of traditional monotonic slow roll inflation, the universe expands over numerous short asymmetric cycles due to the…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…
Large entropy fluctuations in an equilibrium steady state of classical mechanics were studied in extensive numerical experiments on a simple 2--freedom strongly chaotic Hamiltonian model described by the modified Arnold cat map. The rise…
In this paper we study the dynamics and ergodic theory of certain economic models which are implicitly defined. We consider 1-dimensional and 2-dimensional overlapping generations models, a cash-in-advance model, heterogeneous markets and a…
In this paper we advance the entropy theory of discrete nonautonomous dynamical systems that was initiated by Kolyada and Snoha in 1996. The first part of the paper is devoted to the measure-theoretic entropy theory of general topological…
Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance…
We show one possible dynamical approach to the study of the distribution of prime numbers. Our approach is based on two complexity methods, the Computable Information Content and the Entropy Information Gain, looking for analogies between…
Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better…
Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -- in order to uncover their key features -- we have to turn to empirical methods, one of which was recently…
We propose that chaotic Glass networks (a class of piecewise-linear Ordinary Differential Equations) are good candidates for the design of true random number generators. A Glass network design has the advantage of involving only standard…