Sharpness of the Phase Transition for the Orthant Model

Beekenkamp, Thomas (2021): Sharpness of the Phase Transition for the Orthant Model. In: Mathematical Physics Analysis and Geometry, Vol. 24, No. 4, 36

Abstract

The orthant model is a directed percolation model on 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1385-0172
• Language: English