Comparison and Disjoint-occurrence Inequalities for Random-cluster Models

  title={Comparison and Disjoint-occurrence Inequalities for Random-cluster Models},
  author={Geoffrey Grimmett},
Geoffrey Grimmett Abstra t. A principal technique for studying percolation, (ferromagnetic) Ising, Potts, and random-cluster models is the FKG inequality, which implies certain stochastic comparison inequalities for the associated probability measures. The first result of this paper is a new comparison inequality, proved using an argument developed in Refs. 2, 6, 14, and 21 in order to obtain strict inequalities for critical values. As an application of this inequality, we prove that the… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 22 references

Percolation. Springer-Verlag, New York

  • G. R. Grimmett
  • 1989
Highly Influential
6 Excerpts

The random-cluster model. Probability, Statistics and Optimisation (F

  • G. R. Grimmett
  • 1994

Some remarks on the Berg–Kesten inequality (to appear)

  • M. Talagrand
  • 1993
1 Excerpt

Strict monotonicity for critical points in percolation and ferromagnetic models

  • M. Aizenman, G. R. Grimmett
  • Journal of Statistical Physics
  • 1991

On a combinatorial conjecture concerning disjoint occurrences of events

  • Berg, J. van den, U. Fiebig
  • Annals of Probability
  • 1987

Quantitative estimates and rigorous inequalities for critical points of a graph and its subgraphs

  • M. V. Menshikov
  • Theory of Probability and its Applications
  • 1987

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