Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations
Dynamical Systems
2026-03-04 v2 Geometric Topology
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.
Cite
@article{arxiv.2412.20627,
title = {Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations},
author = {Lien-Yung Kao and Giuseppe Martone},
journal= {arXiv preprint arXiv:2412.20627},
year = {2026}
}
Comments
The exposition has been improved to enhance clarity and readability