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The Voter Model

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

Abstract

The voter model is the spin system with rates c(x,η) given by
$$ c(x,\eta ) = \left\{ {\begin{array}{*{20}c} {\sum\limits_y {p(x,y)\eta (y)} } & {if{\text{ }}\eta (x) = 0,} \\ {\sum\limits_y {p(x,y)[1 - \eta (y)]} } & {f{\text{ }}\eta (x) = 1,} \\ \end{array} } \right. $$
(0.1)
where p(x,y) ≥ 0 for x, yS and
$$ \begin{array}{*{20}c} {\sum\limits_y {p(x,y) = 1} } & {for{\text{ }}x{\text{ }} \in {\text{ }}S.} \\ \end{array} $$

Keywords

Markov Chain Random Walk Invariant Measure Ergodic Theorem Voter Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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