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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.19224 |
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| _version_ | 1866912653439401984 |
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| author | Anderson, Nickolas Elkin, Moriah Kelley, Elizabeth Ovenhouse, Nicholas Wright, Kayla |
| author_facet | Anderson, Nickolas Elkin, Moriah Kelley, Elizabeth Ovenhouse, Nicholas Wright, Kayla |
| contents | The classical dimer model is concerned with the (weighted) enumeration of perfect matchings of a graph. An $n$-dimer cover is a multiset of edges that can be realized as the disjoint union of $n$ individual matchings. For a probability measure recently defined by Douglas, Kenyon, and Shi, which we call the $M_n$-dimer model, we study random $n$-dimer covers on bipartite graphs with matrix edge weights and produce formulas for local edge statistics and correlations. We also classify local moves that can be used to simplify the analysis of such graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local Statistics of the $M_n$-Dimer Model Anderson, Nickolas Elkin, Moriah Kelley, Elizabeth Ovenhouse, Nicholas Wright, Kayla Combinatorics Probability 82B20, 05C70 The classical dimer model is concerned with the (weighted) enumeration of perfect matchings of a graph. An $n$-dimer cover is a multiset of edges that can be realized as the disjoint union of $n$ individual matchings. For a probability measure recently defined by Douglas, Kenyon, and Shi, which we call the $M_n$-dimer model, we study random $n$-dimer covers on bipartite graphs with matrix edge weights and produce formulas for local edge statistics and correlations. We also classify local moves that can be used to simplify the analysis of such graphs. |
| title | Local Statistics of the $M_n$-Dimer Model |
| topic | Combinatorics Probability 82B20, 05C70 |
| url | https://arxiv.org/abs/2508.19224 |