Inhomogeneity and universality: off-critical behavior of interfaces

2009/07/09 by Pierre Nolin, Nolin, Pierre · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.0907.1495

17 pages, 5 figures

arxiv created 2009/07/09 · openalex publication_date 2009/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We further study the interfaces arising in a situation of inhomogeneity. More precisely, we identify a characteristic length for the gradient percolation model, that enables us to tighten previous estimates established for it. This allows to construct non-trivial scaling limits: the limiting objects share some properties with critical percolation interfaces, but locally, they rather behave like off-critical percolation interfaces.

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