Vanishing of the anchored isoperimetric profile in bond percolation at p c

2019/03/19 by Cerf, Raphaël, Dembin, Barbara, Raphaël Cerf +1
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1903.08065

openalex publication_date 2019/03/19 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We consider the anchored isoperimetric profile of the infinite open cluster, defined for p > p_c, whose existence has been recently proved in [3]. We extend adequately the definition for p = p_c, in finite boxes. We prove a partial result which implies that, if the limit defining the anchored isoperimetric profile at p_c exists, it has to vanish.

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