Scaling limit of a drainage network model on perturbed lattice

2023/02/19 by Rahul Roy, Roy, Rahul, Kumarjit Saha +3
Mathematics · Physics and Astronomy · Computer Science · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Data Management and Algorithms

paper · pdf · doi:10.48550/arxiv.2302.09489

Abstract

Study of random networks generally requires the nodes to be independently and uniformly distributed such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a drainage network model constructed on a randomly perturbed subset of ℤ², where both horizontal and vertical perturbations are given by exponentially decaying unbounded discrete random variables and vertical perturbations are allowed in the upward direction only. We show that the resultant stochastic network is a single tree a.s. We further establish that as a collection of paths, under diffusive scaling the resultant network converges to the Brownian web.

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