The Berger-Wang formula for the Markovian joint spectral radius

DOI10.1016/j.laa.2014.01.022zbMath1321.15021arXiv1401.2711OpenAlexW2107700582MaRDI QIDQ2442449

Victor S. Kozyakin

Publication date: 3 April 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.2711

zbMATH Keywords

generalized spectral radiusjoint spectral radiusBerger-Wang formulainfinite matrix productstopological Markov chains

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

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Cites Work

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• On asymptotic properties of matrix semigroups with an invariant cone
• Extremal and Barabanov semi-norms of a semigroup generated by a bounded family of matrices
• The generalised Berger-Wang formula and the spectral radius of linear cocycles
• Asymptotic stability and generalized Gelfand spectral radius formula
• An explicit Lipschitz constant for the joint spectral radius
• Sets of matrices all infinite products of which converge
• Bounded semigroups of matrices
• The generalized spectral radius and extremal norms
• Symbolic dynamics. One-sided, two-sided and countable state Markov shifts
• Inequalities for numerical invariants of sets of matrices
• Characterization of joint spectral radius via trace
• Joint spectral radius, operator semigroups, and a problem of W. Wojtyński
• The generalized spectral-radius theorem: An analytic-geometric proof
• Stability of discrete linear inclusion
• Exact computation of joint spectral characteristics of linear operators
• Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
• Formulae for joint spectral radii of sets of operators
• Joint Spectral Characteristics of Matrices: A Conic Programming Approach
• Corrigendum/addendum to: Sets of matrices all infinite products of which converge