Sharpness of the phase transition for the corrupted compass model on transitive graphs

Beekenkamp, Thomas

doi:10.1016/j.indag.2021.03.005

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2021

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“…More recently, a revolutionary technique using the OSSS inequality was developed by Duminil-Copin, Raoufi and Tassion to prove sharp thresholds in models with more complexities [5][6][7][8]. These models include the random cluster model, Voronoi percolation, Boolean percolation, Gaussian fields, the corrupted compass model and the Widom-Rowlinson model [3,4,15,17].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Sharpness of the Phase Transition for the Orthant Model

Beekenkamp

2021

Math Phys Anal Geom

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The orthant model is a directed percolation model on $\mathbb {Z}^{d}$ ℤ d , in which all clusters are infinite. We prove a sharp threshold result for this model: if p is larger than the critical value above which the cluster of 0 is contained in a cone, then the shift from 0 that is required to contain the cluster of 0 in that cone is exponentially small. As a consequence, above this critical threshold, a shape theorem holds for the cluster of 0, as well as ballisticity of the random walk on this cluster.

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