A generalized Cheeger inequality and the Steklov Problem on finite graphs
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911141243912192 |
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| author | Hua, Bobo Kamtue, Supanat Liu, Shiping Münch, Florentin Peyerimhoff, Norbert |
| author_facet | Hua, Bobo Kamtue, Supanat Liu, Shiping Münch, Florentin Peyerimhoff, Norbert |
| contents | We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Cheeger inequalities for Steklov eigenvalues. In particular, we get a sharp estimate for the first non-trivial Steklov eigenvalue via Escobar Cheeger constant. At the end, we extend Hassannezhad and Miclo's convergence result to non-reversible Markov chains via a different method based on resolvent convergence, answering one of their questions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalized Cheeger inequality and the Steklov Problem on finite graphs Hua, Bobo Kamtue, Supanat Liu, Shiping Münch, Florentin Peyerimhoff, Norbert Differential Geometry Probability 53A70 (Primary) 05C50, 15A42, 39A12, 60J28, 60J35, 60J50 (Secondary) We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Cheeger inequalities for Steklov eigenvalues. In particular, we get a sharp estimate for the first non-trivial Steklov eigenvalue via Escobar Cheeger constant. At the end, we extend Hassannezhad and Miclo's convergence result to non-reversible Markov chains via a different method based on resolvent convergence, answering one of their questions. |
| title | A generalized Cheeger inequality and the Steklov Problem on finite graphs |
| topic | Differential Geometry Probability 53A70 (Primary) 05C50, 15A42, 39A12, 60J28, 60J35, 60J50 (Secondary) |
| url | https://arxiv.org/abs/2509.05667 |