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, Bd. 24, Nr. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1385-0172
• Sprache: Englisch