The contact process on a tree: Behavior near the first phase transition

C. Chris Wu

doi:10.1016/0304-4149(94)00080-D

The contact process on a tree: Behavior near the first phase transition

C. Chris Wu

Penn State Beaver

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We study the critical behavior of the contact process on a homogeneous tree. It is shown that if the degree of the tree is greater than four, then the survival probability θ(λ) behaves like (λ - λ_c)^β with β = 1 when λ is near but above the critical point λ_c, and the expected infection time χ(λ) behaves like (λ_c - λ)^-γ with γ = 1 when λ is near but below λ_c. Analogous results for the oriented percolation model are also obtained.

Original language	English (US)
Pages (from-to)	99-112
Number of pages	14
Journal	Stochastic Processes and their Applications
Volume	57
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(94)00080-D
State	Published - May 1995

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/0304-4149(94)00080-D

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title = "The contact process on a tree: Behavior near the first phase transition",

abstract = "We study the critical behavior of the contact process on a homogeneous tree. It is shown that if the degree of the tree is greater than four, then the survival probability θ(λ) behaves like (λ - λc)β with β = 1 when λ is near but above the critical point λc, and the expected infection time χ(λ) behaves like (λc - λ)-γ with γ = 1 when λ is near but below λc. Analogous results for the oriented percolation model are also obtained.",

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note = "Funding Information: Supported in part by a Research Development Grant from the Penn State University. *E-mail: [email protected].",

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N1 - Funding Information: Supported in part by a Research Development Grant from the Penn State University. *E-mail: [email protected].

PY - 1995/5

Y1 - 1995/5

N2 - We study the critical behavior of the contact process on a homogeneous tree. It is shown that if the degree of the tree is greater than four, then the survival probability θ(λ) behaves like (λ - λc)β with β = 1 when λ is near but above the critical point λc, and the expected infection time χ(λ) behaves like (λc - λ)-γ with γ = 1 when λ is near but below λc. Analogous results for the oriented percolation model are also obtained.

AB - We study the critical behavior of the contact process on a homogeneous tree. It is shown that if the degree of the tree is greater than four, then the survival probability θ(λ) behaves like (λ - λc)β with β = 1 when λ is near but above the critical point λc, and the expected infection time χ(λ) behaves like (λc - λ)-γ with γ = 1 when λ is near but below λc. Analogous results for the oriented percolation model are also obtained.

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U2 - 10.1016/0304-4149(94)00080-D

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AN - SCOPUS:0002988718

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

The contact process on a tree: Behavior near the first phase transition

Abstract

All Science Journal Classification (ASJC) codes

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