Backbone scaling limits for random walks on random critical trees

2017/05/16 by Gérard Ben Arous, Arous, Gérard Ben, Manuel Cabezas +3
Mathematics · Physics and Astronomy · #60F17 #60K37 #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1705.05883

openalex publication_date 2017/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as randomly trapped random walks (as defined in [BCČR15]) and thus describe these scaling limits as spatially subordinated Brownian motions

Related

• Scaling limit of critical percolation clusters on hyperbolic random half-planar triangulations and the associated random walks
• Scaling limit for the random walk on critical lattice trees
• Scaling limits for random walks on long range percolation clusters
• Backbone scaling limit of the high-dimensional IIC
• On breadth-first constructions of scaling limits of random graphs and random unicellular maps