Spectral Entropy via Random Spanning Forests

Carlo Nicolini

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arXiv · 2512.13318

Spectral Entropy via Random Spanning Forests

Carlo Nicolini

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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.

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Carlo Nicolini. 2025-12-15. Spectral Entropy via Random Spanning Forests. https://arxiv.org/abs/2512.13318

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