2020/02/29 by Subhroshekhar Ghosh, Kumarjit Saha · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Brownian motion #Complex Network Analysis Techniques #Computational Geometry and Mesh Generation #Lattice (music) #Point process #Poisson distribution #Poisson point process #Scaling #Stochastic geometry #Stochastic processes and statistical mechanics #Transmission (telecommunications) #Wireless sensor network #math.PR #stat.ML
paper · pdf · doi:10.1007/s10955-020-02604-1
published in Journal of Statistical Physics 180(1-6), 1167-1205 (Springer Science+Business Media) · We improved the exposition of our approach to cover lattice perturbations that are uniform in the unit Euclidean cube. In this version we added many figures to explain our argument better
arxiv created 2020/05/26 · openalex publication_date 2020/07/09 · openalex created_date 2020/07/16 · arxiv updated 2020/08/26 · openalex updated_date 2026/08/05
Stochastic networks based on random point sets as nodes have attracted considerable interest in many applications, particularly in communication networks, including wireless sensor networks, peer-to-peer networks and so on. The study of such networks generally requires the nodes to be independently and uniformly distributed as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate the stochastic geometry of networks obtained from directed spanning forests (DSF) based on randomly perturbed lattices, which have desirable statistical properties as a models of spatially dependent point fields. In the regime of low disorder, we show in 2D and 3D that the DSF almost surely consists of a single tree. In 2D, we further establish that the DSF, as a collection of paths, converges under diffusive scaling to the Brownian web.