Spectral Independence
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913317228904448 |
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| author | Golsefidy, Alireza S Mallahi-Karai, Keivan Mohammadi, Amir |
| author_facet | Golsefidy, Alireza S Mallahi-Karai, Keivan Mohammadi, Amir |
| contents | We prove the spectral gap property for random walks on the product of two non-locally isomorphic analytic real or p-adic compact groups with simple Lie algebras, under the necessary condition that the marginals posses a spectral gap. Furthermore, we give additional control on the spectral gap depending on certain specific properties of the given groups and marginals; in particular, we prove some new cases of the super-approximation conjecture. One ingredient of the proof is a local Ulam stability result which is introduced and proved in this paper. This result characterizes partially defined almost homomorphisms between two analytic compact groups with simple Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral Independence Golsefidy, Alireza S Mallahi-Karai, Keivan Mohammadi, Amir Group Theory Dynamical Systems We prove the spectral gap property for random walks on the product of two non-locally isomorphic analytic real or p-adic compact groups with simple Lie algebras, under the necessary condition that the marginals posses a spectral gap. Furthermore, we give additional control on the spectral gap depending on certain specific properties of the given groups and marginals; in particular, we prove some new cases of the super-approximation conjecture. One ingredient of the proof is a local Ulam stability result which is introduced and proved in this paper. This result characterizes partially defined almost homomorphisms between two analytic compact groups with simple Lie algebras. |
| title | Spectral Independence |
| topic | Group Theory Dynamical Systems |
| url | https://arxiv.org/abs/2404.10873 |