Subdiffusive concentration for the chemical distance in Bernoulli percolation

2024/06/21 by Van Hao Can, Can, Van Hao, Van Quyet Nguyen +1
Mathematics · #82B43 #82D30 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 60K37 #Probability (math.PR) #Random Matrices and Applications #Secondary 60K35 #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2406.14834

openalex publication_date 2024/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Considering supercritical Bernoulli percolation on ℤ^d, Garet and Marchand [GM09] proved a diffusive concentration for the graph distance. In this paper, we sharpen this result by establishing the subdiffusive concentration inequality, which revisits the sublinear bound of the variance proved by Dembin [Dem22] as a consequence. Our approach is inspired by similar work in First-passage percolation [BR08, DHS14], combined with new tools to address the challenge posed by the infinite weight of the model. These tools, including the notion of effective radius and its properties, enable a simple one-step renormalization process as a systematic means of managing the effects of resampling edges.

Related

• Chemical subdiffusivity of critical 2D percolation
• Limiting distribution of the chemical distance in high dimensional critical percolation
• Moderate deviations for the chemical distance in Bernoulli percolation
• Déviations modérées de la distance chimique
• The diffusivity of supercritical Bernoulli percolation is infinitely differentiable