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Universality of the Brownian net

2024/01/17 by Rongfeng Sun, Sun, Rongfeng, Jan M. Swart +3
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2401.09370

openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Brownian web is a collection of one-dimensional coalescing Brownian motions starting from every point in space and time, while the Brownian net is an extension that also allows branching. We show here that the Brownian net is the universal scaling limit of one-dimensional branching-coalescing random walks with weak binary branching and arbitrary increment distributions that have finite (3+ε)-th moment. This gives the first example in the domain of attraction of the Brownian net where paths can cross without coalescing.

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