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21 10 IM Probability NotíciaTítulo: On the convergence of the Drainage Network Model with Branching

Palestrante: Rafael Souza dos Santos (IM-UFRJ)
Data: 25/10/2021
Horário: 15:00hrs às 16:00hrs
Local: Transmissão online

Confira AQUI o link para a transmissão.

Resumo: We introduce the Drainage Network with Branching, which is a system of coalescing random walks with paths that can branch and that exhibit some dependence before coalescence. It extends the Drainage Network model introduced by Gangopadhyay, Roy and Sarkar in 2004, by allowing the paths to branch. We also study the convergence of  the Drainage Network with Branching, under diffusive scaling, to the Brownian Web or Net, according to specific conditions for the branching probability. We show that based on the specification of the branching probability, we can have convergence to the Brownian Web or we can have a tight family such that any weak limit point contains a Brownian Net. In the latter case, we conjecture that the limit is indeed the Brownian Net. This is a joint work with Glauco Valle (IM-UFRJ) and Leonel Zuaznabar (IME-USP).

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