Displaying similar documents to “The σ -algebra of pasts of a random walk on the orbits of the Bernoulli action of the group ℤ d .”

A new approach to mutual information

Fumio Hiai, Dénes Petz (2007)

Banach Center Publications

Similarity:

A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.

Amenability of linear-activity automaton groups

Gideon Amir, Omer Angel, Bálint Virág (2013)

Journal of the European Mathematical Society

Similarity:

We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group – the mother group – has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.

Isomorphic random Bernoulli shifts

V. Gundlach, G. Ochs (2000)

Colloquium Mathematicae

Similarity:

We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.

High order approximation of probabilistic shock profiles in hyperbolic conservation laws with uncertain initial data

Christoph Schwab, Svetlana Tokareva (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We analyze the regularity of random entropy solutions to scalar hyperbolic conservation laws with random initial data. We prove regularity theorems for statistics of random entropy solutions like expectation, variance, space-time correlation functions and polynomial moments such as gPC coefficients. We show how regularity of such moments (statistical and polynomial chaos) of random entropy solutions depends on the regularity of the distribution law of the random shock location of the...

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica

Similarity:

Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.

On the entropy for group actions on the circle

Eduardo Jorquera (2009)

Fundamenta Mathematicae

Similarity:

We show that for a finitely generated group of C² circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.