Gibbs partitions and lattice paths
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916970981490688 |
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| author | Bosio, Niccolò Kuba, Markus Stufler, Benedikt |
| author_facet | Bosio, Niccolò Kuba, Markus Stufler, Benedikt |
| contents | This work is devoted to the analysis of a Gibbs partition model, also known as a composition scheme. We consider a natural new condition on the component weights. It leads to a new behavior for the total number of components. We discover a condensation phenomenon, producing a unique giant component comprising almost the entire mass. Additionally, we prove a point process limit describing the asymptotic size of the non-maximal components exhibiting a sublinear power-law growth. A particular motivation for our article stems from applications, ranging from simple random walks in the cube, over lattice paths models in the plane, pairs of directed random walks, over to urn models and card guessing games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gibbs partitions and lattice paths Bosio, Niccolò Kuba, Markus Stufler, Benedikt Combinatorics 05A15, 05A16, 60F05, 60C05 This work is devoted to the analysis of a Gibbs partition model, also known as a composition scheme. We consider a natural new condition on the component weights. It leads to a new behavior for the total number of components. We discover a condensation phenomenon, producing a unique giant component comprising almost the entire mass. Additionally, we prove a point process limit describing the asymptotic size of the non-maximal components exhibiting a sublinear power-law growth. A particular motivation for our article stems from applications, ranging from simple random walks in the cube, over lattice paths models in the plane, pairs of directed random walks, over to urn models and card guessing games. |
| title | Gibbs partitions and lattice paths |
| topic | Combinatorics 05A15, 05A16, 60F05, 60C05 |
| url | https://arxiv.org/abs/2411.03930 |