Work

On the Convergence of the Drainage Network with Branching

Year: 2024

Type: article

Abstract: The Drainage Network is a system of coalescing random walks, exhibiting long-range dependence before coalescence, introduced by Gangopadhyay, Roy, and Sarkar [14]. Coletti, Fontes, and Dias [5] proved its convergence to the Brownian Web under diffusive scaling. In this work, we introduce a perturbation of the system allowing branching of the random walks with low probabilities varying with the scaling parameter. When the branching probability is inversely proportional to the scaling parameter, we show that this drainage network with branching consists of a tight family such that any weak limit point contains a Brownian Net. We conjecture that the limit is indeed the Brownian Net.

Source: Markov Processes And Related Fields

DOI: 10.61102/1024-2953-mprf.2024.30.2.001

Authors: R. Santos, G. Valle, L. Zuaznabar

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro

Awards: G1384181827, G1840770272, G228631196, G322153650, G5425476681, G6807369351, G8522711164

OpenAlex ID: W4401897464

FWCI:

Cites: 25

Cited by:

Related to: 10