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Ergodicity and Mixing Properties

Encyclopedia of Complexity and Systems Science

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FormalPara Glossary
Bernoulli shift:

Mathematical abstraction of the scenario in statistics or probability in which one performs repeated independent identical experiments.

Markov chain:

A probability model describing a sequence of observations made at regularly spaced time intervals such that at each time, the probability distribution of the subsequent observation depends only on the current observation and not on prior observations.

Measure-preserving transform at ion:

A map from a measure space to itself such that for each measurable subset of the space, it has the same measure as its inverse image under the map.

Measure-theoretic entropy:

A nonnegative (possibly infinite) real number describing the complexity of a measure-preserving transformation.

Product transformation:

Given a pair of measure-preserving transformations: T of X and S of Y, the product transformation is the map of X × Y given by (T × S)(x, y) = (T(x), S(y)).

Definition of the Subject

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  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada

    Anthony Quas

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    Robert A. Meyers

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Quas, A. (2017). Ergodicity and Mixing Properties. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_175-2

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  1. Latest

    Ergodicity and Mixing Properties
    Published:
    12 March 2023

    DOI: https://doi.org/10.1007/978-3-642-27737-5_175-3

  2. Original

    Ergodicity and Mixing Properties
    Published:
    11 August 2017

    DOI: https://doi.org/10.1007/978-3-642-27737-5_175-2

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