Inhomogeneous contact processes on trees

Details Inhomogeneous contact processes on trees Inhomogeneous contact processes on trees

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jsp....88.1399w&link_type=abstract

Journal of Statistical Physics, Volume 88, Issue 5-6, pp. 1399-1408

Physics

Contact Process, Inhomogeneity, Trees

Scientific paper

We consider an inhomogeneous contact process on a treemathbb{T}_k of degree k, where the infection rate at any site is λ, the death rate at any site inS subset mathbb{T}_k is δ (with 0 < δ ⩽ 1) and that at any site inmathbb{T}_k - S is 1. Denote byλ _c (mathbb{T}_k ) the critical value for the homogeneous model (i.e., δ=1) onmathbb{T}_k and by ϑ( δ, λ) the survival probability of the inhomogeneous model onmathbb{T}_k . We prove that when k > 4, ifS = mathbb{T}_σ , a subtree embedded inmathbb{T}_k , with 1 ⩽ σ ⩽ √ k, then three exists δ {c/σ} strictly between (λ _c (mathbb{T}_k )/λ _c (mathbb{T}_σ )) and 1 such that (θ (δ ,λ _c (mathbb{T}_k )) = 0) when δ > δ {c/σ} and ϑ( δ, λ c(θ (δ , λ _c (mathbb{T}_k )) > 0) > 0 when δ < δ {c/σ}; if S={ o}, the origin ofθ (δ , λ _c (mathbb{T}_k )) = 0, thenθ (δ , λ _c (mathbb{T}_k )) = 0 for any δ ɛ (0, 1).

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