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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2512.03015 |
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| _version_ | 1866909940440891392 |
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| author | Peterson, Carsten |
| author_facet | Peterson, Carsten |
| contents | With a view towards studying the multitemporal wave equation on affine buildings recently introduced by Anker-Rémy-Trojan [arXiv:2312.06860], we systematically develop the basic properties of the discrete wave equation on $\mathbb{Z}$ and use this to explain existing results about the wave equation on regular graphs. Furthermore, we explicitly compute the incoming and outgoing translation representations and the scattering operator, in the sense of Lax-Phillips, for regular and biregular trees. Finally, we use the wave equation on biregular graphs to extend a result of Brooks-Lindenstrauss about delocalization of eigenfunctions on regular graphs to the setting of biregular graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The discrete wave equation with applications to scattering theory and quantum chaos Peterson, Carsten Spectral Theory Mathematical Physics Combinatorics 35L05, 05C50, 43A85, 35P25, 81Q50, 33C52 With a view towards studying the multitemporal wave equation on affine buildings recently introduced by Anker-Rémy-Trojan [arXiv:2312.06860], we systematically develop the basic properties of the discrete wave equation on $\mathbb{Z}$ and use this to explain existing results about the wave equation on regular graphs. Furthermore, we explicitly compute the incoming and outgoing translation representations and the scattering operator, in the sense of Lax-Phillips, for regular and biregular trees. Finally, we use the wave equation on biregular graphs to extend a result of Brooks-Lindenstrauss about delocalization of eigenfunctions on regular graphs to the setting of biregular graphs. |
| title | The discrete wave equation with applications to scattering theory and quantum chaos |
| topic | Spectral Theory Mathematical Physics Combinatorics 35L05, 05C50, 43A85, 35P25, 81Q50, 33C52 |
| url | https://arxiv.org/abs/2512.03015 |