2022/07/11 by Tom Hutchcroft, Hutchcroft, Tom
Mathematics · #FOS: Mathematics #Geometry and complex manifolds #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2207.05226
openalex publication_date 2022/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish several equivalent characterisations of the anchored isoperimetric dimension of supercritical clusters in Bernoulli bond percolation on transitive graphs. We deduce from these characterisations together with a theorem of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that if G is a transient transitive graph then the infinite clusters of Bernoulli percolation on G are transient for p sufficiently close to 1. It remains open to extend this result down to the critical probability. Along the way we establish two new cluster repulsion inequalities that are of independent interest.