Sadel CH, Schulz-Baldes H (2010)
Publication Type: Journal article, Original article
Publication year: 2010
Publisher: Institute of Mathematical Statistics (IMS)
Book Volume: 38
Pages Range: 2224-2257
URI: http://de.arxiv.org/abs/0802.2909
DOI: 10.1214/10-AOP544
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. © Institute of Mathematical Statistics, 2010.
APA:
Sadel, C.H., & Schulz-Baldes, H. (2010). Random Lie Group actions on compact manifolds: a perturbative analysis. Annals of Probability, 38, 2224-2257. https://dx.doi.org/10.1214/10-AOP544
MLA:
Sadel, Christian Hermann, and Hermann Schulz-Baldes. "Random Lie Group actions on compact manifolds: a perturbative analysis." Annals of Probability 38 (2010): 2224-2257.
BibTeX: Download