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arXiv · 2011.00902

Lyapunov exponents and stability properties of higher rank representations

Florestan Martin-Baillon
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Abstract

Generalizing results of Deroin-Dujardin, we introduce the notion of proximal stability for a holomorphic family $ (\rho_{\lambda}) $ of representations $ \Gamma \to \text{SL}(d, \mathbb{C}) $, where $ \Gamma $ 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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Florestan Martin-Baillon. 2020-11-02. Lyapunov exponents and stability properties of higher rank representations. https://arxiv.org/abs/2011.00902

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