The Contact Process

  • Thomas M. Liggett
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 276)


The contact process is the spin system in which S = Z d and
$$ c(x,\eta ) = \left\{ {\begin{array}{*{20}c} {\lambda \sum\limits_{|y - x| = 1} {\eta (y)} } & {if{\text{ }}\eta (x) = 0,} \\ 1 & {f{\text{ }}\eta (x) = 1,} \\ \end{array} } \right. $$
where λ is a nonnegative parameter. One interpretation of this process is as a model for the spread of an infection. An individual at x ∈ S is infected if η(x) = 1 and healthy if η (x) = 0. Healthy individuals become infected at a rate which is proportional to the number of infected neighbors. Infected individuals recover at a constant rate, which is normalized to be 1.


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Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

  • Thomas M. Liggett
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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