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arXiv · 2501.19286

Analyticity of the Lyapunov exponents of random products of matrices

Artur Amorim·Marcelo Durães·Aline Melo
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Abstract

This paper is concerned with the study of random (Bernoulli and Markovian) product of matrices on a compact space of symbols. We establish the analyticity of the maximal Lyapunov exponent as a function of the transition probabilities, thus extending the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols. Our approach combines the spectral properties of the associated Markov operator with the theory of holomorphic functions in Banach spaces.

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Artur Amorim, Marcelo Durães, Aline Melo. 2025-01-31. Analyticity of the Lyapunov exponents of random products of matrices. https://arxiv.org/abs/2501.19286

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