Random Lie group actions on compact manifolds: A perturbative analysis

Details Random Lie group actions on compact manifolds: A perturbative analysis Random Lie group actions on compact manifolds: A perturbative analysis

2008-02-20

arxiv.org/abs/0802.2909v3

Annals of Probability 2010, Vol. 38, No. 6, 2224-2257

Physics

Mathematical Physics

Published in at http://dx.doi.org/10.1214/10-AOP544 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Random Lie group actions on compact manifolds: A perturbative analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Random Lie group actions on compact manifolds: A perturbative analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Random Lie group actions on compact manifolds: A perturbative analysis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-648108