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- W2944196977 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." @default.
- W2944196977 created "2019-05-16" @default.
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- W2944196977 date "2019-05-07" @default.
- W2944196977 modified "2023-09-27" @default.
- W2944196977 title "Random Self-Similar Trees: A mathematical theory of Horton laws" @default.
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