Choosing a Spanning Tree for the Integer Lattice Uniformly
| dc.creator | Pemantle, Robin | |
| dc.date | 2004-04-02 | |
| dc.date.accessioned | 2026-07-07T05:07:02Z | |
| dc.date.available | 2026-07-07T05:07:02Z | |
| dc.description | Consider the nearest neighbor graph for the integer lattice Z^d in d dimensions. For a large finite piece of it, consider choosing a spanning tree for that piece uniformly among all possible subgraphs that are spanning trees. As the piece gets larger, this approaches a limiting measure on the set of spanning graphs for Z^d. This is shown to be a tree if and only if d=<4. In this case, the tree has only one topological end, i.e. there are no doubly infinite paths. When d>=5 the spanning forest has infinitely many components almost surely, with each component having one or two topological ends. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404043 | |
| dc.identifier | http://arxiv.org/abs/math/0404043 | |
| dc.identifier | Ann. Probab., 19, 1559 - 1574 (1991) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70700 | |
| dc.subject | Probability | |
| dc.subject | 60C05 (Primary) 60K35 (Secondary) | |
| dc.title | Choosing a Spanning Tree for the Integer Lattice Uniformly | |
| dc.type | text |