The lowest crossing in two-dimensional critical percolation
van den Berg, J. ; Járai, A. A.
Ann. Probab., Tome 31 (2003) no. 1, p. 1241-1253 / Harvested from Project Euclid
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We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the lowest occupied crossing $R_n$ from the half-line left of A to the half-line right of B. We show that the probability that $R_n$ has a site at distance smaller than m from $\mathit{AB}$ is of order $(\log (n/m))^{-1}$, uniformly in $1 \leq m \leq n/2$. Much of our analysis can be carried out for other two-dimensional lattices as well.
Publié le : 2003-07-14
Classification:  Critical percolation,  lowest crossing,  critical exponent.,  60K35 
@article{1055425778,
     author = {van den Berg, J. and J\'arai, A. A.},
     title = {The lowest crossing in two-dimensional critical percolation},
     journal = {Ann. Probab.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 1241-1253},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1055425778}
}

van den Berg, J.; Járai, A. A. The lowest crossing in two-dimensional critical percolation. Ann. Probab., Tome 31 (2003) no. 1, pp.  1241-1253. http://gdmltest.u-ga.fr/item/1055425778/