Concept

Ergodicity

Related publications (69)

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Polarization and Channel Ordering: Characterizations and Topological Structures

Rajai Nasser

Information theory is the field in which we study the fundamental limitations of communication. Shannon proved in 1948 that there exists a maximum rate, called capacity, at which we can reliably communicate information through a given channel. However, Sha ...

EPFL2017

Breaking Lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering

Hatice Altug, Kosmas Tsakmakidis

A century-old tenet in physics and engineering asserts that any type of system, having bandwidth Delta omega, can interact with a wave over only a constrained time period Delta t inversely proportional to the bandwidth (Delta t-Delta w similar to 2 pi). Th ...

2017

An Ergodic Theory of Binary Operations-Part I: Key Properties

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization (in the general multilevel sense) when they are used in Arikan style constructions. This paper, which is presented in two parts, solves this probl ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Nematodynamics and random homogenization

Tudor Ratiu

We study the homogenization problem for the system of equations of dynamics of a mixture of liquid crystals with random structure. We consider a simplified form of the Ericksen-Leslie equations for an incompressible medium with inhomogeneous density with r ...

Taylor & Francis2016

Ergodic Theory Meets Polarization I: A Foundation of Polarization Theory

Rajai Nasser

An open problem in polarization theory is to determine the binary operations that always lead to polarization when they are used in Arıkan style constructions. This paper solves this problem by providing a necessary and sufficient condition for a binary op ...

IEEE2015

High order numerical approximation of the invariant measure of ergodic SDEs

Assyr Abdulle, Gilles Vilmart

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...

Society for Industrial and Applied Mathematics2014

Are atmospheric surface layer f lows ergodic?

Valentin Simeonov, Martin Froidevaux, Marc Parlange, Gabriel George Katul, Chad Higgins

The transposition of atmospheric turbulence statistics from the time domain, as conventionally sampled in field experiments, is explained by the so-called ergodic hypothesis. In micrometeorology, this hypothesis assumes that the time average of a measured ...

American Geophysical Union2013

Cantor systems, piecewise translations and simple amenable groups

Nicolas Monod

We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suita ...

Annal Mathematics2013

Quasi-equilibria in reduced Liouville spaces

David Lyndon Emsley

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a rest ...

AMER INST PHYSICS2012

The research program of Stochastic Deformation (with a view toward Geometric Mechanics)

This is an overview of a program of stochastic deformation of the mathematical tools of classical mechanics, in the Lagrangian and Hamiltonian approaches. It can also be regarded as a stochastic version of Geometric Mechanics.The main idea is to construct ...

2012