Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nucleation scaling in jigsaw percolation   Jigsaw percolation is a nonlocal process that iteratively merges connected
clusters in a deterministic "puzzle graph" by using connectivity properties of
a random "people graph" on the same set of vertices. We presume the
Erdos--Renyi people graph with edge probability p and investigate the
probability that the puzzle is solved, that is, that the process eventually
produces a single cluster. In some generality, for puzzle graphs with N
vertices of degrees about D (in the appropriate sense), this probability is
close to 1 or small depending on whether pD(log N) is large or small. The one
dimensional ring and two dimensional torus puzzles are studied in more detail
and in many cases the exact scaling of the critical probability is obtained.
The paper settles several conjectures posed by Brummitt, Chatterjee, Dey, and
Sivakoff who introduced this model.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
3
The categories of this paper are: physics