Spectrum Estimation through Kirchhoff Random Forests
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912772189585408 |
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| author | Barthelmé, Simon Castell, Fabienne Gaudillière, Alexandre Mélot, Clothilde Quattropani, Matteo Tremblay, Nicolas |
| author_facet | Barthelmé, Simon Castell, Fabienne Gaudillière, Alexandre Mélot, Clothilde Quattropani, Matteo Tremblay, Nicolas |
| contents | Given a non-oriented edge-weighted graph, we show how to make some estimation of the associated Laplacian eigenvalues through Monte Carlo evaluation of spectral quantities computed along Kirchhoff random rooted spanning forest trajectories. The sampling cost of this estimation is only linear in the node number, up to a logarithmic factor. By associating a double cover of such a graph with any symmetric real matrix, we can then perform spectral estimation in the same way for the latter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectrum Estimation through Kirchhoff Random Forests Barthelmé, Simon Castell, Fabienne Gaudillière, Alexandre Mélot, Clothilde Quattropani, Matteo Tremblay, Nicolas Probability 65F15, 05C50, 68W20 G.2.2 Given a non-oriented edge-weighted graph, we show how to make some estimation of the associated Laplacian eigenvalues through Monte Carlo evaluation of spectral quantities computed along Kirchhoff random rooted spanning forest trajectories. The sampling cost of this estimation is only linear in the node number, up to a logarithmic factor. By associating a double cover of such a graph with any symmetric real matrix, we can then perform spectral estimation in the same way for the latter. |
| title | Spectrum Estimation through Kirchhoff Random Forests |
| topic | Probability 65F15, 05C50, 68W20 G.2.2 |
| url | https://arxiv.org/abs/2507.19164 |