The Fourier spectrum of critical percolation

@article{Garban2008TheFS,
  title={The Fourier spectrum of critical percolation},
  author={Christophe Garban and G{\'a}bor Pete and Oded Schramm},
  journal={Acta Mathematica},
  year={2008},
  volume={205},
  pages={19-104}
}
Consider the indicator function f of a 2-dimensional percolation crossing event. In this paper, the Fourier transform of f is studied and sharp bounds are obtained for its lower tail in several situations. Various applications of these bounds are derived. In particular, we show that the set of exceptional times of dynamical critical site percolation on the triangular grid in which the origin percolates has dimension ${\frac{31}{36}}$ almost surely, and the corresponding dimension in the half… 
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