2024/04/08 by Reimer Kühn, Kuehn, Reimer
Computer Science · Mathematics · Physics and Astronomy · #Bayesian Methods and Mixture Models #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2404.05503
openalex publication_date 2024/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous micro-structure of the percolation problem, i.e., a self-consistent determination of locally varying percolation probabilities. This is achieved using a cavity or message passing approach. It can be evaluated, both for single large instances of locally tree-like graphs, and in the thermodynamic limit of random graphs of finite mean degree in the configuration model class.