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Michael Aizenman coauthored tree-diagram inequalities for percolation with Charles M. Newman. Their work controls multipoint connectivity and gives a condition for the percolation susceptibility exponent to take its mean-field value. The method relates large-scale critical behavior to convergence properties of diagrams built from pairwise connection probabilities.^[ref]

By Michael Aizenman, Charles M. Newman.

Journal of Statistical Physics 36(1–2), 107–143. Author/institutional record collaborate.princeton.edu/en/publications/tree-graph-inequalities-and-critical-behavior-in-percolation-mode/ confirms diagrammatic convergence criterion for susceptibility exponent gamma=1.