2020/01/19 by Joseph Horan, Horan, Joseph · 1 citation
Mathematics · Physics and Astronomy · #15A18 (Secondary) #37A30 (Primary) 37A25 #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2001.06788
openalex publication_date 2020/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a sequence of matrices that are associated to Markov dynamical systems and use determinant-free linear algebra techniques (as well as some algebra and complex analysis) to rigorously estimate the eigenvalues of every matrix simultaneously without doing any calculations on the matrices themselves. As a corollary, we obtain mixing rates for every system at once, as well as symmetry properties of densities associated to the system; we also find the spectral properties of a sequence of related factor systems.