Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local Bootstrap Percolation   We study a variant of bootstrap percolation in which growth is restricted to
a single active cluster. Initially there is a single active site at the origin,
while other sites of Z^2 are independently occupied with small probability p,
otherwise empty. Subsequently, an empty site becomes active by contact with 2
or more active neighbors, and an occupied site becomes active if it has an
active site within distance 2. We prove that the entire lattice becomes active
with probability exp[alpha(p)/p], where alpha(p) is between -pi^2/9 + c sqrt p
and pi^2/9 + C sqrt p (-log p)^3. This corrects previous numerical predictions
for the scaling of the correction term.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph