Analyticity of the pressure function for products of matrices
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913639002275840 |
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| author | Hautecœur, Arnaud |
| author_facet | Hautecœur, Arnaud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analyticity of the pressure function for products of matrices Hautecœur, Arnaud Probability Mathematical Physics Dynamical Systems Functional Analysis 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. |
| title | Analyticity of the pressure function for products of matrices |
| topic | Probability Mathematical Physics Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2501.03590 |