EVOLUTIONARY FORMALISM FOR PRODUCTS OF POSITIVE RANDOM MATRICES
成果类型：
Article
署名作者：
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
署名单位：
University of Bremen; Harvard University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004975
发表日期：
1994
页码：
859-901
关键词：
摘要：
We present a formalism to investigate directionality principles in evolution theory for populations, the dynamics of which can be described by a positive matrix cocycle (product of random positive matrices). For the latter, we establish a random version of the Perron-Frobenius theory which extends all known results and enables us to characterize the equilibrium state of a corresponding abstract symbolic dynamical system by an extremal principle. We develop a thermodynamic formalism for random dynamical systems, and in this framework prove that the top Lyapunov exponent is an analytic function of the generator of the cocycle. On this basis a fluctuation theory for products of positive random matrices can be developed which leads to an inequality in dynamical entropy that can be interpreted as a directionality principle for the mutation and selection process in evolutionary dynamics.
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