Critical percolation on slabs with random columnar disorder

2024/08/20 by M. Castro, Castro, Matheus B., Rémy Sanchis +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2408.10927

openalex publication_date 2024/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore a bond percolation model on slabs \mathbbS⁺_k=ℤ₊× ℤ₊×\0,…,k\ featuring one-dimensional inhomogeneities. In this context, a vertical column on the slab comprises the set of vertical edges projecting to the same vertex on ℤ₊×\0,…,k\. Columns are chosen based on the arrivals of a renewal process, where the tail distributions of inter-arrival times follow a power law with exponent ϕ>1. Inhomogeneities are introduced as follows: vertical edges on selected columns are open (closed) with probability q (respectively 1-q), independently. Conversely, vertical edges within unselected columns and all horizontal edges are open (closed) with probability p (respectively 1-p). We prove that for all sufficiently large ϕ (depending solely on k), the following assertion holds: if q>p_c(\mathbbS⁺_k), then p can be taken strictly smaller than p_c(\mathbbS⁺_k) in a manner that percolation still occurs.

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