The devil's staircase for chip-firing on random graphs and on graphons
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2020
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914912999047168 |
|---|---|
| author | Kiss, Viktor Levine, Lionel Tóthmérész, Lilla |
| author_facet | Kiss, Viktor Levine, Lionel Tóthmérész, Lilla |
| contents | We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erdős--Rényi random graph. We show that in various situations the resulting activity diagrams converge to a devil's staircase as we increase the number of vertices. Our method is to generalize the parallel chip-firing to graphons, and to prove a continuity result for the activity. We also show that the activity of a chip configuration on a graphon does not necessarily exist, but it does exist for every chip configuration on a large class of graphons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_13104 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The devil's staircase for chip-firing on random graphs and on graphons Kiss, Viktor Levine, Lionel Tóthmérész, Lilla Combinatorics Dynamical Systems Probability 82C20 (Primary) 05C80, 26A30, 60J05 (Secondary) We study the behavior of the activity of the parallel chip-firing upon increasing the number of chips on an Erdős--Rényi random graph. We show that in various situations the resulting activity diagrams converge to a devil's staircase as we increase the number of vertices. Our method is to generalize the parallel chip-firing to graphons, and to prove a continuity result for the activity. We also show that the activity of a chip configuration on a graphon does not necessarily exist, but it does exist for every chip configuration on a large class of graphons. |
| title | The devil's staircase for chip-firing on random graphs and on graphons |
| topic | Combinatorics Dynamical Systems Probability 82C20 (Primary) 05C80, 26A30, 60J05 (Secondary) |
| url | https://arxiv.org/abs/2004.13104 |