A correlation inequality for connection events in percolation

@inproceedings{Berg1999ACI,
  title={A correlation inequality for connection events in percolation},
  author={Jacob van den Berg and Jonas Kahn},
  year={1999}
}
It is well-known in percolation theory (and intuitively plausible) that two events of the form “there is an open path from s to a” are positively correlated. We prove the (not intuitively obvious) fact that this is still true if we condition on an event of the form “there is no open path from s to t”. 1991 Mathematics Subject Classification: 05C99 60C05 60K35. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-6 of 6 references

A lower bound for the critical probability in a certain percolation process

  • T. E. Harris
  • Proc. Cam. Phil. Soc. 56
  • 1960
Highly Influential
5 Excerpts

Percolation

  • G. Grimmett
  • Springer, New York
  • 1989

Combinatorics

  • B. Bollobás
  • Cambridge Univ. Pr., Cambridge
  • 1986
1 Excerpt

An inequality for the weights of two families of sets

  • R. Ahlswede, D. E. Daykin
  • their unions and intersections, Z. Wahrscheinl…
  • 1978
1 Excerpt

An inequality for the weights of two families of sets , their unions and intersections

  • Ahlswede, D. E. Daykin
  • Z . Wahrscheinl . Geb .

Similar Papers

Loading similar papers…