Lyapunov exponents and stability properties of higher rank representations

2020/11/02 by Florestan Martin-Baillon, Martin-Baillon, Florestan
Mathematics · #Advanced Algebra and Geometry #Mathematical Dynamics and Fractals #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2011.00902

Abstract

Generalizing results of Deroin-Dujardin, we introduce the notion of proximal stability for a holomorphic family (ρ_λ) of representations Γ→ SL(d, ℂ) , where Γ is a finitely generated group, and show that it is equivalent to the pluriharmonicity of Lyapunov exponents of the family (defined using random walks).

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