Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K-independent percolation on trees   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.

21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio