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November 2010 Random Lie group actions on compact manifolds: A perturbative analysis
Christian Sadel, Hermann Schulz-Baldes
Ann. Probab. 38(6): 2224-2257 (November 2010). DOI: 10.1214/10-AOP544

Abstract

A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg’s irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r.t. a unique smooth measure on the manifold up to errors of the order of the coupling constant. Applications to the theory of products of random matrices and a model of a disordered quantum wire are presented.

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Christian Sadel. Hermann Schulz-Baldes. "Random Lie group actions on compact manifolds: A perturbative analysis." Ann. Probab. 38 (6) 2224 - 2257, November 2010. https://doi.org/10.1214/10-AOP544

Information

Published: November 2010
First available in Project Euclid: 24 September 2010

zbMATH: 1223.60053
MathSciNet: MR2683629
Digital Object Identifier: 10.1214/10-AOP544

Subjects:
Primary: 37H05 , 37H15 , 60J05

Keywords: Birkhoff sum , group action , invariant measure

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 6 • November 2010
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