Invariant splitting of a slab into infinitely many robust clusters

2024/01/29 by Péter Mester, Mester, Péter
Mathematics · #60K35 #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2401.16357

openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an example of an invariant bond percolation process on the slab ℤ²× \0,1\ with the property that it has infinitely many clusters whose critical percolation probability is strictly less than 1. We also show that no such process can exist in ℤ².

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