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Abstract: A random Lie group action on a compact manifold generates a discrete timeMarkov process. The main object of this paper is the evaluation of associatedBirkhoff sums in a regime of weak, but sufficiently effective coupling of therandomness. This effectiveness is expressed in terms of random Lie algebraelements and replaces the transience or Furstenberg-s irreducibility hypothesisin related problems. The Birkhoff sum of any given smooth function then turnsout to be equal to its integral w.r.t. a unique smooth measure on the manifoldup to errors of the order of the coupling constant. Applications to the theoryof products of random matrices and a model of a disordered quantum wire arepresented.



Author: Christian Sadel, Hermann Schulz-Baldes

Source: https://arxiv.org/



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