Using Householder Matrices to Establish Mixing Test Critical Values

A measure-preserving dynamical system can be approximated by a Markov shift with a bistochastic matrix. This leads to using empirical stochastic matrices to measure and estimate properties of stirring protocols. Specifically, the second largest eigenvalue can be used to statistically decide if a sti...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2012-10
Main Author: Smith, Aaron Carl
Format: Article
Language:English
Subjects:
Eigenvalues
Markov processes
Mixing tests
Stirring
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A measure-preserving dynamical system can be approximated by a Markov shift with a bistochastic matrix. This leads to using empirical stochastic matrices to measure and estimate properties of stirring protocols. Specifically, the second largest eigenvalue can be used to statistically decide if a stirring protocol is weak-mixing, ergodic, or nonergodic. Such hypothesis tests require appropriate probability distributions. In this paper, we propose using Monte Carlo empirical probability distributions from unistochastic matrices to establish critical values. These unistochastic matrices arise from randomly constructed Householder matrices.
ISSN:2331-8422