Mathematical Physics Seminar, University of Arizona, April 19, 2000 Title: "A Limit Theorem for Subcritical Percolation" Speaker: Martin Bazant (MIT) Abstract: Beginning with certain scaling assumptions related to the recent results of Borgs, Chayes, Kesten and Spencer, it is shown that the probability distribution of the largest-cluster size in subcritical percolation on a finite lattice of size N converges to the Fisher-Tippett (or Gumbel) distribution exp(-exp(-z)) in a certain weak sense as N -> oo. As a corollary, it is shown that the variance of the largest-cluster size is bounded. The proof uses ``renormalization group'' ideas adapted from the statistical theory of extremes with correlations controlled by the FKG inequality. Note: this lecture addresses certain "gory details" behind the general ideas to be presented in the Applied Mathematics Colloquium on April 21.