Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Topological Minors in Random Simplicial Complexes   For random graphs, the containment problem considers the probability that a
binomial random graph $G(n,p)$ contains a given graph as a substructure. When
asking for the graph as a topological minor, i.e., for a copy of a subdivision
of the given graph, it is well-known that the (sharp) threshold is at $p=1/n$.
We consider a natural analogue of this question for higher-dimensional random
complexes $X^k(n,p)$, first studied by Cohen, Costa, Farber and Kappeler for
$k=2$.
  Improving previous results, we show that $p=\Theta(1/\sqrt{n})$ is the
(coarse) threshold for containing a subdivision of any fixed complete
$2$-complex. For higher dimensions $k>2$, we get that $p=O(n^{-1/k})$ is an
upper bound for the threshold probability of containing a subdivision of a
fixed $k$-dimensional complex.

18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat