most recent 30 from http://mathoverflow.net 2013-05-22T21:55:11Z http://mathoverflow.net/feeds/user/27025 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108906/avalanche-principle-for-higher-dimensional-unimodular-matrices Silvius 2012-10-05T12:03:05Z 2012-11-06T09:40:15Z

<p>Hello everyone,</p> <p>I have a quick question for people working on quasi-periodic Schrodinger operators, Lyapunov exponents for Schrodinger cocycles or in other fields that might make them aware of this topic. There is an inductive tool used to prove positivity or continuity of the Lyapunov exponent called the Avalanche Principle. It says something about the growth of large products of $SL_2(\mathbb{R})$ matrices. </p> <p>Does anyone know if this principle has been extended in some form to higher dimensional matrices? If so, can you point me to a paper where it appears? I would like/need to extend it myself, but if the work has been done already, I'd rather not repeat it. </p> <p>Thanks.</p>

http://mathoverflow.net/questions/108906/avalanche-principle-for-higher-dimensional-unimodular-matrices/111630#111630 Silvius 2012-11-16T20:26:51Z 2012-11-16T20:26:51Z

Hey Matheus, thanks a lot for your answer. Well, it turns out that someone else in the community had a similar version of the AP as well, and my collaborator and I also figured out an extension. But I am grateful for your pointing out to me W. Schlag's paper, as the problem he solves there would have been our next project :)