Nearest-Particle Systems

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


Nearest-particle systems are one-dimensional spin systems in which the flip rates depend on η in a certain way which we will now describe. Configurations η ∈ X = {0,1}Z1 will be given an occupancy interpretation: η(x) = 1 means that there is a particle at x, and η( x) = 0 means that x is vacant. For x ∈ Z1 and η ∈ X, let lx (η) and rx (η) be the distances from x to the nearest particle to the left and right respectively:
$$ \begin{array}{*{20}c} {lx(\eta ) = x - \max \{ y < x:\eta (y) = 1\} ,{\text{ }}and} \\ {rx(\eta ) = \min (y > x:\eta (y) = 1\} - x.} \\ \end{array} $$


Invariant Measure Total Birth Rate Infinite System Finite System Contact Process 
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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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