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No percolation at criticality

2018/07/10 by Achillefs Tzioufas, Tzioufas, Achillefs
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1807.03849

openalex publication_date 2018/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ever since J.M. Hammersley showed the existence of phase-transitions regarding independent bond percolation on general d ≥ 2 dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most prominent and long-standing basic open problem in the subsequently extensively developed theory of percolation.

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