An approximation for return time distributions of random walks on sparse networks
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916794539704320 |
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| author | Hormann, Erik Lambiotte, Renaud Cantwell, George T. |
| author_facet | Hormann, Erik Lambiotte, Renaud Cantwell, George T. |
| contents | We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours respectively. We test this approximation on several classes of large graphs and find excellent agreement between our approximations and the true distributions. While the statistical properties of a random walk will depend on the structure of the network, the observed agreement between our approximations and numerical calculations implies that while local structure is clearly very influential, global structure is only important in a relatively superficial way, namely through the total number of edges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An approximation for return time distributions of random walks on sparse networks Hormann, Erik Lambiotte, Renaud Cantwell, George T. Social and Information Networks We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours respectively. We test this approximation on several classes of large graphs and find excellent agreement between our approximations and the true distributions. While the statistical properties of a random walk will depend on the structure of the network, the observed agreement between our approximations and numerical calculations implies that while local structure is clearly very influential, global structure is only important in a relatively superficial way, namely through the total number of edges. |
| title | An approximation for return time distributions of random walks on sparse networks |
| topic | Social and Information Networks |
| url | https://arxiv.org/abs/2405.20166 |