Random self-similar trees: A mathematical theory of Horton laws

Autor(es)

Kovchegov, Yevgeniy ^[1] ; Zaliapin, Ilya ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: PROBABILITY SURVEYS; v. 17, p. 1-211, 2020.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 18/07826-5 - Limites hidrodinâmicos de processos coalescentes e árvores de extensão mínima com aplicações em biologia matemática
• Beneficiário: Anatoli Iambartsev
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional