Tightness and tails of the maximum in 3D Ising interfaces

  title={Tightness and tails of the maximum in 3D Ising interfaces},
  author={Reza Gheissari and Eyal Lubetzky},
  journal={arXiv: Probability},
Consider the 3D Ising model on a box of side length $n$ with minus boundary conditions above the $xy$-plane and plus boundary conditions below it. At low temperatures, Dobrushin (1972) showed that the interface separating the predominantly plus and predominantly minus regions is localized: its height above a fixed point has exponential tails. Recently, the authors proved a law of large numbers for the maximum height $M_n$ of this interface: for every $\beta$ large, $M_n/ \log n\to c_\beta$ in… Expand
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