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Ergodicity of canonical Gibbs measures with respect to the diffeomorphism group

✍ Scribed by Tobias Kuna; José Luis Silva

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
221 KB
Volume
271
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

For general potentials we prove that every canonical Gibbs measure on configurations over a manifold X is quasi‐invariant w.r.t. the group of diffeomorphisms on X. We show that this quasi‐invariance property also characterizes the class of canonical Gibbs measures. From this we conclude that the extremal canonical Gibbs measures are just the ergodic ones w.r.t. the diffeomorphism group. Thus we provide a whole class of different irreducible representations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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