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D. Ioffe

Title: Random walk representation and fluctuation theory of phase separation lines.

Abstract: In a variety of lattice modles of statistical mechanics the effective probabilistic structure of two-point functions (high temperature) and of phase boundaries (two dimensions, low temperature) is that of a random walk with rapid decorrelation between the steps. Recent rigorous results include a comprehensive version of the Ornstein-Zernike theory for percolation models and finite range ferromagnetic models with pair interactions well as an invariance principle for the phase separation lines in the two dimensional