• Corpus ID: 236447419

High-dimensional near-critical percolation and the torus plateau

@inproceedings{Hutchcroft2021HighdimensionalNP,
  title={High-dimensional near-critical percolation and the torus plateau},
  author={Tom Hutchcroft and Emmanuel Michta and Gordon Slade},
  year={2021}
}
We consider percolation on Z and on the d-dimensional discrete torus, in dimensions d ≥ 11 for the nearest-neighbour model and in dimensions d > 6 for spread-out models. For Z, we employ a wide range of techniques and previous results to prove that there exist positive constants c and C such that the slightly subcritical two-point function and one-arm probabilities satisfy Ppc−ε(0↔ x) ≤ C ‖x‖d−2 e−cε ‖x‖ and c r2 e−Cε r ≤ Ppc−ε ( 0↔ ∂[−r, r] ) ≤ C r2 e−cε 1/2r. Using this, we prove that… 

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