Spectrum Estimation through Kirchhoff Random Forests

Fuente: arXiv
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Bibliographic Details
Main Authors: Barthelmé, Simon, Castell, Fabienne, Gaudillière, Alexandre, Mélot, Clothilde, Quattropani, Matteo, Tremblay, Nicolas
Format: Preprint
Published: 2025
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_version_ 1866912772189585408
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