TY - JOUR
T1 - K-independent percolation on trees
AU - Mathieu, Pierre
AU - Temmel, C.
PY - 2015
Y1 - 2015
N2 - Consider the class of k-independent bond or site percolations with parameter p on a tree T. We derive tight bounds on p for both almost sure percolation and almost sure 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 Balister & Bollobs for 1-independent bond percolations. Central to our argumentation are moment method bounds la Lyons supplemented by explicit percolation models la Balister & Bollobs. An indispensable tool is the minimality and explicit construction of Shearer's measure on the k-fuzz of Z. © 2011 Elsevier B.V. All rights reserved.
AB - Consider the class of k-independent bond or site percolations with parameter p on a tree T. We derive tight bounds on p for both almost sure percolation and almost sure 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 Balister & Bollobs for 1-independent bond percolations. Central to our argumentation are moment method bounds la Lyons supplemented by explicit percolation models la Balister & Bollobs. An indispensable tool is the minimality and explicit construction of Shearer's measure on the k-fuzz of Z. © 2011 Elsevier B.V. All rights reserved.
UR - https://www.scopus.com/pages/publications/84857626492
UR - https://www.scopus.com/inward/citedby.url?scp=84857626492&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2011.10.014
DO - 10.1016/j.spa.2011.10.014
M3 - Article
SN - 0304-4149
VL - 122
SP - 1129
EP - 1153
JO - Stochastic Processes and Their Applications
JF - Stochastic Processes and Their Applications
IS - 3
ER -
