Bai-Pollicott Algorithm for Markovian Products of Positive Matrices

2019/04/11 by Fan Wang, David Steinsaltz, Wang, Fan +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1904.05560

openalex publication_date 2019/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We consider the problem of estimating the top Lyapunov exponents for Markovian products of positive matrices. We define a new transfer operator as a matrix of classical transfer operators and prove its spectral properties. With the spectral properties, we generalize (and provide a more theoretically rigorous foundation for) an algorithm that was introduced informally by Bai and formally by Pollicott based on dynamical zeta functions.

Citations

• Products of Random Matrices
• Random matrix products and measures on projective spaces

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