Critical scaling profile for trees and connected subgraphs on the complete graph
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913170162974720 |
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| author | Liu, Yucheng Slade, Gordon |
| author_facet | Liu, Yucheng Slade, Gordon |
| contents | We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a critical window. Our motivation comes from the analysis of the finite-size scaling of lattice trees and lattice animals on a high-dimensional discrete torus, for which we conjecture that the identical profile applies in dimensions $d \ge 8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical scaling profile for trees and connected subgraphs on the complete graph Liu, Yucheng Slade, Gordon Probability Mathematical Physics Combinatorics 05C30, 60K35, 82B41 We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a critical window. Our motivation comes from the analysis of the finite-size scaling of lattice trees and lattice animals on a high-dimensional discrete torus, for which we conjecture that the identical profile applies in dimensions $d \ge 8$. |
| title | Critical scaling profile for trees and connected subgraphs on the complete graph |
| topic | Probability Mathematical Physics Combinatorics 05C30, 60K35, 82B41 |
| url | https://arxiv.org/abs/2412.05503 |