Spectrum Estimation through Kirchhoff Random Forests
Probability
2025-12-19 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2507.19164,
title = {Spectrum Estimation through Kirchhoff Random Forests},
author = {Simon Barthelmé and Fabienne Castell and Alexandre Gaudillière and Clothilde Mélot and Matteo Quattropani and Nicolas Tremblay},
journal= {arXiv preprint arXiv:2507.19164},
year = {2025}
}
Comments
35 pages, 16 figures