Non-Markovian heat flows on directed hypergraphs
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908619631493120 |
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| author | Mugnolo, Delio |
| author_facet | Mugnolo, Delio |
| contents | We introduce a semigroup framework for Laplacians on directed hypergraphs, extending the classical heat flow models on graphs and establishing hypergraphs as prototypical models for non-Markovian diffusion. We apply spectral surgery methods to derive eigenvalue bounds, thus describing large-time behaviour of the heat flow. Unlike on standard graphs, heat flows on directed hypergraphs may lose positivity and/or $\infty$-contractivity, yet can recover them eventually or asymptotically under specific combinatorial configurations: examples based on duals of oriented graph and realisations of the Fano plane illustrate these phenomena.
Our approach combines combinatorial, order-theoretic and linear-algebraic methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Markovian heat flows on directed hypergraphs Mugnolo, Delio Dynamical Systems Analysis of PDEs Combinatorics 47D06, 05C50, 05C65, 39A12 We introduce a semigroup framework for Laplacians on directed hypergraphs, extending the classical heat flow models on graphs and establishing hypergraphs as prototypical models for non-Markovian diffusion. We apply spectral surgery methods to derive eigenvalue bounds, thus describing large-time behaviour of the heat flow. Unlike on standard graphs, heat flows on directed hypergraphs may lose positivity and/or $\infty$-contractivity, yet can recover them eventually or asymptotically under specific combinatorial configurations: examples based on duals of oriented graph and realisations of the Fano plane illustrate these phenomena. Our approach combines combinatorial, order-theoretic and linear-algebraic methods. |
| title | Non-Markovian heat flows on directed hypergraphs |
| topic | Dynamical Systems Analysis of PDEs Combinatorics 47D06, 05C50, 05C65, 39A12 |
| url | https://arxiv.org/abs/2510.17497 |