Random Matrices and Lyapunov Coefficients Regularity

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• 作者：Giovanni Gallavotti
• 关键词：Lyapunov exponents ; Cluster expansion ; Fisher model ; Statistical mechanic ; Thermodynamic formalism
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：166
• 期：3-4
• 页码：558-574
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

Analyticity and other properties of the largest or smallest Lyapunov exponent of a product of real matrices with a “cone property” are studied as functions of the matrices entries, as long as they vary without destroying the cone property. The result is applied to stability directions, Lyapunov coefficients and Lyapunov exponents of a class of products of random matrices and to dynamical systems. The results are not new and the method is the main point of this work: it is is based on the classical theory of the Mayer series in Statistical Mechanics of rarefied gases.