The paper establishes explicit Hölder moduli of continuity for Lyapunov exponents of random GL(2,R) cocycles under compact support and simple spectrum, identifies specific log-Hölder exponents, proves concentration inequalities, and extends the theory to higher dimensions and one-dimensional random
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math.DS 2years
2026 2verdicts
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The top Lyapunov exponent of random products of matrices in GL(d,R) is shown to be real-analytic in the weights p and entries A, with explicit polydisc radii in C^N and closed-form Cauchy bounds derived from a single Kato perturbation on the complexified Markov operator.
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Quantitative H\"older Regularity, Concentration, and Spectral Applications for Lyapunov Exponents of Random $\operatorname{GL}(2,\mathbb{R})$ Cocycles, with Extensions to $\operatorname{GL}(d,\mathbb{R})$
The paper establishes explicit Hölder moduli of continuity for Lyapunov exponents of random GL(2,R) cocycles under compact support and simple spectrum, identifies specific log-Hölder exponents, proves concentration inequalities, and extends the theory to higher dimensions and one-dimensional random
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Quantitative Analyticity for Lyapunov Exponents of Random Products of Matrices with Explicit Polydiscs and Cauchy Coefficient Bounds
The top Lyapunov exponent of random products of matrices in GL(d,R) is shown to be real-analytic in the weights p and entries A, with explicit polydisc radii in C^N and closed-form Cauchy bounds derived from a single Kato perturbation on the complexified Markov operator.