Analyticity of the pressure function for products of matrices
Probability
2025-01-08 v1 Mathematical Physics
Dynamical Systems
Functional Analysis
math.MP
Abstract
The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In this paper, we prove the analyticity of the pressure function for products of non-invertible matrices satisfying an irreducibility and a contractivity assumptions. Additionally, we establish a variational principle for the pressure function, thereby generalizing previous results.
Keywords
Cite
@article{arxiv.2501.03590,
title = {Analyticity of the pressure function for products of matrices},
author = {Arnaud Hautecœur},
journal= {arXiv preprint arXiv:2501.03590},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2402.03879 by other authors