On the spectral gap of the path graph in the limit of large volume
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909657592758272 |
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| author | Kerner, Joachim Yatsyna, Pavlo |
| author_facet | Kerner, Joachim Yatsyna, Pavlo |
| contents | In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external potential, it is shown that the spectral gap converges to zero strictly faster than it does for the free Laplacian. The underlying mechanism is a combination of the increase in volume and an effective degeneracy of the ground state in the limiting regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_08910 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the spectral gap of the path graph in the limit of large volume Kerner, Joachim Yatsyna, Pavlo Spectral Theory 34L15, 05C38, 15A18, 49R50 In this paper we study the spectral gap of the path graph and illustrate an interesting effect which has been described recently in the continuous setting. More explicitly, in the large-volume limit and in the presence of a certain external potential, it is shown that the spectral gap converges to zero strictly faster than it does for the free Laplacian. The underlying mechanism is a combination of the increase in volume and an effective degeneracy of the ground state in the limiting regime. |
| title | On the spectral gap of the path graph in the limit of large volume |
| topic | Spectral Theory 34L15, 05C38, 15A18, 49R50 |
| url | https://arxiv.org/abs/2106.08910 |