Convergence to the Brownian Web for a generalization of the drainage network model

TL;DR

This paper proves that a generalized model of coalescing random walks with long-range jumps converges to the Brownian Web under diffusive scaling, extending understanding of complex stochastic systems.

Contribution

It introduces a new class of coalescing random walks with crossing paths and dependence, demonstrating their convergence to the Brownian Web.

Findings

Convergence of the generalized random walks to the Brownian Web

Inclusion of long-range jumps and crossing paths in the model

Establishment of conditions for convergence under diffusive scaling

Abstract

We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing crossing paths and exibiting dependence before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.