AbstractWe study the Ising model on Z^3 with an externel field {\epsilon h_v} where h_v~N(0,1). We want to show that for any T lower than the critical temperature T_c, the long range order exsits as long as \epsilon is sufficiently small depending on T. This work extends previous results of Imbrie (1985) and Bricmont–Kupiainen (1988) from the very low temperature regime to the entire low tempe...
Description: The central-limit type results are universal in many random walk models: they are known as Donsker’s theorem for the classical Zd random walk, and also hold for some random walks in random environment, even when the environment is degenerate like percolation. In their proofs, the homogenization theory, which comes from PDE, plays an important role. This course will cover the follo...