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CHOOSING A SPANNING TREE FOR THE INTEGER LATTICE UNIFORMLY Running Head : RANDOM SPANNING TREES
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pemantle, Robin |
| Copyright Year | 1991 |
| Abstract | Consider the nearest neighbor graph for the integer lattice Z 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. 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.math.upenn.edu/~pemantle/papers/spanning.pdf |
| Alternate Webpage(s) | http://www.math.upenn.edu/~pemantle/papers/spanning.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0404043v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Choose (action) File spanning Graph - visual representation Integer (number) Large Single Linkage Cluster Analysis Spanning tree Tree (data structure) Trees (plant) |
| Content Type | Text |
| Resource Type | Article |
