Search results for "ergodic theory"

Uniformly ergodic A-contractions on Hilbert spaces

2009

Structure of distributions generated by the scenery flow

2015

We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution in the sense of Hochman is generated by a uniformly scaling measure, which provides a converse to a regularity theorem on the structure of distributions generated by the scenery flow. We further show that the collection of fractal distributions is closed under the weak topology and, moreover, is a Poulsen simplex, that is, extremal points are dense. We apply these to show that a Baire generic measure is as far as possible from being uniformly scaling: at almost all points, it has all fractal distributions as tangent …

A generalized method for the design of ergodic sum-of-cisoids simulators for multiple uncorrelated rayleigh fading channels

2010

In this paper, we present a new method for the design of ergodic sum-of-sinusoids (SOS) simulation models for multiple uncorrelated Rayleigh fading channels. The method, which is intended for a special class of SOS models, known as sum-of-cisoids (SOC) models, can be used to generate an arbitrary number of uncorrelated Rayleigh fading waveforms with specified Doppler power spectral characteristics. This is in contrast to the SOS simulators currently available in the open literature that have been designed under the isotropic scattering assumption, which are limited to the simulation of uncorrelated channels characterized by Clarke's U-shaped Doppler power spectral density (DPSD). The excell…

FOUNDATIONS OF FRACTIONAL DYNAMICS

1995

Time flow in dynamical systems is reconsidered in the ultralong time limit. The ultralong time limit is a limit in which a discretized time flow is iterated infinitely often and the discretization time step is infinite. The new limit is used to study induced flows in ergodic theory, in particular for subsets of measure zero. Induced flows on subsets of measure zero require an infinite renormalization of time in the ultralong time limit. It is found that induced flows are given generically by stable convolution semigroups and not by the conventional translation groups. This could give new insight into the origin of macroscopic irreversibility. Moreover, the induced semigroups are generated …

Dynamics in stochastic evolutionary models

2016

We characterize transitions between stochastically stable states and relative ergodic probabilities in the theory of the evolution of conventions. We give an application to the fall of hegemonies in the evolutionary theory of institutions and conflict, and illustrate the theory with the fall of the Qing dynasty and the rise of communism in China.

ON HIGH-SKILL AND LOW-SKILL EQUILIBRIA: A MARKOV CHAIN APPROACH

2006

In this paper we propose to study the dynamics of human capital accumulation by means of a Markov chain. We identify the conditions for the emergence of ergodic and nonergodic dynamics, and relate them to various characteristics of an economic system. The model may generate high-skill and low-skill equilibria as well as intermediate situations. Policy implications are also discussed.

Glass transition for dipolar hard spheres: A mode-coupling approach

1998

Abstract We apply the self-consistent mode-coupling equations, which were recently derived for molecular liquids, to a system of dipolar hard spheres. Making use of the direct correlation function in a mean spherical approximation and with a restriction of the rotational quantum number 1 to zero and one, we find three different phases in the η—T phase space. η and T denote the packing fraction and the temperature respectively. There is one phase where both the transitional degrees of freedom (TDOFs) and the orientational degrees of freedom (ODOFs) are ergodic (liquid), another phase with frozen TDOFs and ergodic ODOFs, and a third phase where TDOFs and ODOFs are frozen (glass). The dynamica…

Static freezing transition at a finite temperature in a quasi-one-dimensional deuteron glass.

1996

The dipolar freezing process of a quasi-one-dimensional betaine deuteron glass was studied using linear and nonlinear dielectric spectroscopy. The linear response as measured for frequencies $5\mathrm{mHz}l\ensuremath{\nu}l200\mathrm{MHz}$ was analyzed using the recently invented $\ensuremath{\delta}$ plot, providing evidence for a static freezing transition near 30 K. Measurements of the ergodic to nonergodic transition as well as of the incipient divergence of the nonlinear susceptibility yield independent confirmation of this quasistatic freezing transition temperature. The critical exponent describing the nonlinear behavior is found to be $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\p…

ERGODICITY IN RANDOMLY COLLIDING QUBITS

2009

The dynamics of a single qubit randomly colliding with an environment consisting of just two qubits is discussed. It is shown that the system reaches an equilibrium state which coincides with a pure random state of three qubits. Furthermore the time average and the ensemble averages of the quantities used to characterize the approach to equilibrium (purity and tangles) coincide, a signature of ergodic behavior.

Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators

2018

This paper deals with collisionless transport equationsin bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonallyinvariant velocity measure $\bm{m}(\d v)$ with support $V\subset \R^{d}$ and stochastic partly diffuse boundary operators $\mathsf{H}$ relating the outgoing andincoming fluxes. Under very general conditions, such equations are governedby stochastic $C_{0}$-semigroups $\left( U_{\mathsf{H}}(t)\right) _{t\geq 0}$ on $%L^{1}(\Omega \times V,\d x \otimes \bm{m}(\d v)).$ We give a general criterion of irreducibility of $%\left( U_{\mathsf{H}}(t)\right) _{t\geq 0}$ and we show that, under very natural assumptions, if an …