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 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 δσc 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 > δσc and 0(δ, λc(double-struck T signk)) > 0 when δ < δσc; if S = {0}, the origin of double-struck T signk, then θ(δ, λc(double-struck T signk)) = 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