## Abstract

We consider an inhomogeneous contact process on a tree double-struck T sign k of degree k, where the infection rate at any site is λ, the death rate at any site in S ⊂ double-struck T sign_{k} is δ (with 0 < δ ≤ 1) and that at any site in double-struck T sign_{k} - S is 1. Denote by λ_{c}(double-struck T sign_{k}) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T sign_{k} and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T sign_{k}. We prove that when k > 4, if S = double-struck T sign_{σ}, a subtree embedded in double-struck T sign_{k}, with 1 ≤ σ ≤ √k, then there exists δ^{σ}_{c} strictly between λ_{c}(double-struck T sign_{k})/λ_{c}(double-struck T sign_{σ}) and 1 such that 0(δ λ_{c}(double-struck T sign_{k})) = 0 when δ > δ^{σ}_{c} and 0(δ, λ_{c}(double-struck T sign_{k})) > 0 when δ < δ^{σ}_{c}; if S = {0}, the origin of double-struck T sign_{k}, then θ(δ, λ_{c}(double-struck T sign_{k})) = 0 for any δ ∈ (0, 1).

Original language | English (US) |
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Pages (from-to) | 1399-1408 |

Number of pages | 10 |

Journal | Journal of Statistical Physics |

Volume | 88 |

Issue number | 5-6 |

DOIs | |

State | Published - Sep 1997 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics