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1 results

Critical behavior of percolation and Markov fields on branching planes
Part of
- Equilibrium statistical mechanics
- Special processes
C. Chris Wu
Journal:

Journal of Applied Probability / Volume 30 / Issue 3 / September 1993

Published online by Cambridge University Press:

14 July 2016, pp. 538-547

Print publication:

September 1993
- Article
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For an independent percolation model on , where is a homogeneous tree and is a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probability θ (p) is a continuous function of p at the critical point pc, and the critical exponents , γ, δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields on are also obtained.