Spectral Entropy via Random Spanning Forests
Statistical Mechanics
2025-12-16 v1 Disordered Systems and Neural Networks
Abstract
We establish an exact analytic relation between random spanning forests and the heat-kernel partition function. This identity enables estimation of partition functions, energies, and the Von Neumann entropy by Wilson sampling of forests, avoiding costly Laplacian eigendecompositions. We validate inverse-Laplace reconstructions stabilized by a Stieltjes spectral-density regularization on synthetic networks. The approach is scalable and yields local node and edge thermodynamic descriptors.
Keywords
Cite
@article{arxiv.2512.13318,
title = {Spectral Entropy via Random Spanning Forests},
author = {Carlo Nicolini},
journal= {arXiv preprint arXiv:2512.13318},
year = {2025}
}