A quantitative Burton–Keane estimate under strong FKG condition

@inproceedings{DuminilCopin2016AQB,
  title={A quantitative Burton–Keane estimate under strong FKG condition},
  author={Hugo Duminil-Copin and Dmitry Ioffe and Yvan Velenik},
  year={2016}
}
We consider translationally-invariant percolation models on ZdZd satisfying the finite energy and the FKG properties. We provide explicit upper bounds on the probability of having two distinct clusters going from the endpoints of an edge to distance nn (this corresponds to a finite size version of the celebrated Burton–Keane [Comm. Math. Phys. 121 (1989) 501–505] argument proving uniqueness of the infinite-cluster). The proof is based on the generalization of a reverse Poincare inequality… CONTINUE READING

Figures from this paper.

Citations

Publications citing this paper.

Minimal spanning trees and Stein's method

VIEW 4 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

References

Publications referenced by this paper.
SHOWING 1-10 OF 17 REFERENCES

Duminil-Copin. The self-dual point of the two-dimensional randomcluster model is critical for q ≥ 1

Vincent Beffara, Hugo
  • Probab. Theory Related Fields,
  • 2012
VIEW 1 EXCERPT

Grimmett . Inequalities and entanglements for percolation and random - cluster models

R Geoffrey
  • The random - cluster model , volume 333 of Grundlehren der Mathema - tischen Wissenschaften [ Fundamental Principles of Mathematical Sciences ]
  • 2006