Abstract
AbstractThe 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.
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Mathematical Physics
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