Entropy of some automorphisms of the II1-factor of the free group in infinite number of generators.

Erling Stormer

Displaying similar documents to “Entropy of some automorphisms of the II1-factor of the free group in infinite number of generators.”

The analogues of entropy and of Fisher's information measure in free probability theory, II.

Dan Voiculescu (1994)

Inventiones mathematicae

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The Analogues of Entropy and of Fisher's Information Measure in Free Probability Theory III: The Absence of Cartan Subalgebras.

D. Voiculescu (1996)

Geometric and functional analysis

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The noncommutative Hilbert transform approach to free entropy

Dan Voiculescu (1998)

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The entropy of algebraic actions of countable torsion-free abelian groups

Richard Miles (2008)

Fundamenta Mathematicae

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This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured....