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arXiv · 2412.20627

Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations

Lien-Yung Kao·Giuseppe Martone
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Abstract

We introduce a correlation number for two strictly positive, locally H\"older continuous, independent potentials with strong entropy gaps at infinity on a topologically mixing countable state Markov shift with BIP. We define in this way a correlation number for pairs of cusped Hitchin representations. Furthermore, we explore the connection between the correlation number and the Manhattan curve, along with several rigidity properties of this correlation number.

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Lien-Yung Kao, Giuseppe Martone. 2024-12-30. Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations. https://doi.org/10.1017/etds.2026.10283

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