Avalanche Principle for higher dimensional unimodular matrices ? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T15:02:20Z http://mathoverflow.net/feeds/question/108906 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108906/avalanche-principle-for-higher-dimensional-unimodular-matrices 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 Answer by Matheus for Avalanche Principle for higher dimensional unimodular matrices ? Matheus 2012-11-06T09:40:15Z 2012-11-06T09:40:15Z <p>Dear Silvius, </p> <p>I think the following recent <a href="http://arxiv.org/abs/1211.0648" rel="nofollow">paper of W. Schlag</a> answers your question.</p> <p>Best, </p> <p>Matheus</p>