K-independent percolation on trees

Details K-independent percolation on trees K-independent percolation on trees

2011-03-07

arxiv.org/abs/1103.1291v3

Stochastic Processes and their Applications, Volume 122, Issue 3, March 2012, Pages 1129-1153

Mathematics

Probability

28 pages, 4 figures

Scientific paper

10.1016/j.spa.2011.10.014

Consider the class of k-independent bond, respectively site, percolations with parameter p on an infinite tree T. We derive tight bounds on p for both a.s. percolation and a.s. nonpercolation. The bounds are continuous functions of k and the branching number of T. This extends previous results by Lyons for the independent case (k=0) and by Bollob\`as & Balister for 1-independent bond percolations. Central to our argumentation are moment method bounds \`a la Lyons supplemented by explicit percolation models \`a la Bollob\`as & Balister. An indispensable tool is the minimality and explicit construction of Shearer's measure on the k-fuzz of Z.

Affiliated with

Also associated with

No associations

Rating

K-independent percolation on trees 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 K-independent percolation on trees, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and K-independent percolation on trees will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-607219