Level-Set Percolation of Gaussian Random Fields on Complex Networks
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929305755320320 |
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| author | Kuehn, Reimer |
| author_facet | Kuehn, Reimer |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_05503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Level-Set Percolation of Gaussian Random Fields on Complex Networks Kuehn, Reimer Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics 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. |
| title | Level-Set Percolation of Gaussian Random Fields on Complex Networks |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2404.05503 |