Analyticity of The Lyapunov Exponents of Random Products of Matrices.

RESUMEN: In this talk, we extend the results and methods of Y. Peres from a finite to an infinite (but compact) space of symbols. In other words, we establish the analyticity of the maximal Lyapunov exponent for independent and identically random products of matrices as a function of the transition probabilities. Our approach combines the spectral properties of the associated Markov operator with the theory of holomorphic functions in Banach spaces. This is a joint work with Artur Amorim and Marcelo Durães.

Posted on Aug 1, 2025 in Dynamical Systems, Seminars