### 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 - Jan 1 1997 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*88*(5-6), 1399-1408. https://doi.org/10.1007/BF02732442

}

*Journal of Statistical Physics*, vol. 88, no. 5-6, pp. 1399-1408. https://doi.org/10.1007/BF02732442

**Inhomogeneous contact processes on trees.** / Wu, Chuntao Chris.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Inhomogeneous contact processes on trees

AU - Wu, Chuntao Chris

PY - 1997/1/1

Y1 - 1997/1/1

N2 - 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 signk is δ (with 0 < δ ≤ 1) and that at any site in double-struck T signk - S is 1. Denote by λc(double-struck T signk) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T signk and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T signk. We prove that when k > 4, if S = double-struck T signσ, a subtree embedded in double-struck T signk, with 1 ≤ σ ≤ √k, then there exists δσ c strictly between λc(double-struck T signk)/λc(double-struck T signσ) and 1 such that 0(δ λc(double-struck T signk)) = 0 when δ > δσ c and 0(δ, λc(double-struck T signk)) > 0 when δ < δσ c; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 0 for any δ ∈ (0, 1).

AB - 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 signk is δ (with 0 < δ ≤ 1) and that at any site in double-struck T signk - S is 1. Denote by λc(double-struck T signk) the critical value for the homogeneous model (i.e., δ = 1) on double-struck T signk and by 0(δ, λ) the survival probability of the inhomogeneous model on double-struck T signk. We prove that when k > 4, if S = double-struck T signσ, a subtree embedded in double-struck T signk, with 1 ≤ σ ≤ √k, then there exists δσ c strictly between λc(double-struck T signk)/λc(double-struck T signσ) and 1 such that 0(δ λc(double-struck T signk)) = 0 when δ > δσ c and 0(δ, λc(double-struck T signk)) > 0 when δ < δσ c; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 0 for any δ ∈ (0, 1).

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U2 - 10.1007/BF02732442

DO - 10.1007/BF02732442

M3 - Article

AN - SCOPUS:0031232243

VL - 88

SP - 1399

EP - 1408

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5-6

ER -