Advertisement

Nearest-Particle Systems

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

Abstract

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:
$$ \begin{array}{*{20}c} {lx(\eta ) = x - \max \{ y < x:\eta (y) = 1\} ,{\text{ }}and} \\ {rx(\eta ) = \min (y > x:\eta (y) = 1\} - x.} \\ \end{array} $$

Keywords

Invariant Measure Total Birth Rate Infinite System Finite System Contact Process 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 1985

Authors and Affiliations

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

Personalised recommendations