Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The size of the giant component in random hypergraphs: a short proof   We consider connected components in $k$-uniform hypergraphs for the following
notion of connectedness: given integers $k\ge 2$ and $1\le j \le k-1$, two
$j$-sets (of vertices) lie in the same $j$-component if there is a sequence of
edges from one to the other such that consecutive edges intersect in at least
$j$ vertices.
  We prove that certain collections of $j$-sets constructed during a
breadth-first search process on $j$-components in a random $k$-uniform
hypergraph are reasonably regularly distributed with high probability. We use
this property to provide a short proof of the asymptotic size of the giant
$j$-component shortly after it appears.

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The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int