**
**

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

**Full text not available from 'Open Access LMU'.**

## 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 |

Item ID: | 96894 |

Date Deposited: | 05. Jun 2023, 15:24 |

Last Modified: | 05. Jun 2023, 15:24 |