On the Euler - Poincare Characteristic of the Random Cluster Model,

Ph. Blanchard, D. Gandolfo, J. Ruiz, S. Shlosman

2003, v.9, №4, 523-545


Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. We present here new results about the behaviour of the Euler characteristic of the clusters of the (Fortuin - Kasteleyn) random cluster measure.

Keywords: Euler - Poincare characteristic,Fortuin -Kasteleyn representation,phase transitions,Alexander duality


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