Spectral Entropy via Random Spanning Forests

2025/12/15 by Carlo Nicolini, Nicolini, Carlo
Computer Science · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Graph theory and applications #Neural Networks and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2512.13318

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

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.

Citations

• Matrix-Forest Theorems
• Algorithm 368: Numerical inversion of Laplace transforms [D5]

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