Positivity of Lyapunov Exponents for a Continuous Matrix-Valued Anderson Model
Positivity of Lyapunov Exponents for a Continuous Matrix-Valued Anderson Model
复制标题
连续矩阵值安德森模型的 Lyapunov 指数的正性
DOI：
10.1007/s11040-007-9023-6
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
H. Boumaza
中科院分区：
文献类型：
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作者：
H. Boumaza
研究了一个连续矩阵值Anderson型模型。证明了在（2，+∞）中除离散能量外的所有能量下，该模型的两个主导Lyapunov指数均为正且不同，从而导致在（2，+∞）中不存在绝对连续的谱.这个结果是对Stolz的一个结果的改进。该方法的基础上，结果由Breuillard和Gelander稠密的子群在半单李群，和一个标准的Goldsheid和Margulis，允许奇异伯努利分布。
We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all energies in (2, +∞) except those in a discrete set, which leads to absence of absolutely continuous spectrum in (2, +∞). This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.