| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Oregon State Univ, Dept Math, 2000 SW Campus Way, Corvallis, OR 97331 - USA
[2] Univ Nevada, Dept Math & Stat, 1664 North Virginia St, Reno, NV 89557 - USA
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | PROBABILITY SURVEYS; v. 17, p. 1-211, 2020. |
| Web of Science Citations: | 2 |
| Abstract | |
The Horton laws originated in hydrology with a 1945 paper by Robert E. Horton, and for a long time remained a purely empirical finding. Ubiquitous in hierarchical branching systems, the Horton laws have been rediscovered in many disciplines ranging from geomorphology to genetics to computer science. Attempts to build a mathematical foundation behind the Horton laws during the 1990s revealed their close connection to the operation of pruning - erasing a tree from the leaves down to the root. This survey synthesizes recent results on invariances and self-similarities of tree measures under various forms of pruning. We argue that pruning is an indispensable instrument for describing branching structures and representing a variety of coalescent and annihilation dynamics. The Horton laws appear as a characteristic imprint of self-similarity, which settles some questions prompted by geophysical data. (AU) | |
| FAPESP's process: | 18/07826-5 - Hydrodynamic limits of coalescent processes and minimal spanning trees with applications in mathematical biology |
| Grantee: | Anatoli Iambartsev |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |