Cross-multiplicative coalescent processes and applications

Autor(es)

Kovchegov, Yevgeniy ^[1] ; Otto, Peter T. ^[2] ; Yambartsev, Anatoly ^[3]

Afiliação do(s) autor(es)

^[1] Oregon State Univ, Dept Math, Corvallis, OR 97331 - USA

^[2] Willamette Univ, Dept Math, Salem, OR 97302 - USA

^[3] Univ Sao Paulo, Inst Math & Stat, Dept Stat, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS; v. 18, n. 1, p. 81-106, 2021.
• Citações Web of Science: 0

Resumo

We introduce and analyze a novel type of coalescent processes called cross-multiplicative coalescent that models a system with two types of particles, A and B. The bonds are formed only between the pairs of particles of opposite types with the same rate for each bond, producing connected components made of particles of both types. We analyze and solve the Smoluchowski coagulation system of equations obtained as a hydrodynamic limit of the corresponding Marcus-Lushnikov process. We establish that the cross-multiplicative kernel is a gelling kernel, and find the gelation time. As an application, we derive the limiting mean length of a minimal spanning tree on a complete asymmetric bipartite graph with independent edge weights, distributed uniformly over {[}0, 1]. (AU)

• Processo FAPESP: 16/19286-0 - Estendendo a teoria da convergência fraca para processos coalescentes
• Beneficiário: Anatoli Iambartsev
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional