A short proof of the Harris-Kesten Theorem

Details A short proof of the Harris-Kesten Theorem A short proof of the Harris-Kesten Theorem

2004-10-15

arxiv.org/abs/math/0410359v3

Bulletin of the London Mathematical Society 38 (2006), 470--484.

Mathematics

Probability

17 pages, 9 figures; typos corrected. To appear in the Bulletin of the London Mathematical Society

Scientific paper

10.1112/S002460930601842X

We give a short proof of the fundamental result that the critical probability
for bond percolation in the planar square lattice is equal to 1/2. The lower
bound was proved by Harris, who showed in 1960 that percolation does not occur
at $p=1/2$. The other, more difficult, bound was proved by Kesten, who showed
in 1980 that percolation does occur for any $p>1/2$.

Affiliated with

Also associated with

No associations

Rating

A short proof of the Harris-Kesten Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A short proof of the Harris-Kesten Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A short proof of the Harris-Kesten Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-486690