Random self-similar trees: A mathematical theory of Horton laws
Probability Surveys, ISSN: 1549-5787, Vol: 70, Issue: none, Page: 1-213
2020
- 11Citations
- 5Captures
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Article Description
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.
Bibliographic Details
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85086342290&origin=inward; http://dx.doi.org/10.1214/19-ps331; https://projecteuclid.org/journals/probability-surveys/volume-17/issue-none/Random-self-similar-trees--A-mathematical-theory-of-Horton/10.1214/19-PS331.full; https://dx.doi.org/10.1214/19-ps331; https://projecteuclid.org/access-suspended
Institute of Mathematical Statistics
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