Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exploring hypergraphs with martingales   Recently, we adapted exploration and martingale arguments of Nachmias and
Peres, in turn based on ideas of Martin-L\"of, Karp and Aldous, to prove
asymptotic normality of the number $L_1$ of vertices in the largest component
$C$ of the random $r$-uniform hypergraph throughout the supercritical regime.
In this paper we take these arguments further to prove two new results: strong
tail bounds on the distribution of $L_1$, and joint asymptotic normality of
$L_1$ and the number $M_1$ of edges of $C$. These results are used in a
separate paper "Counting connected hypergraphs via the probabilistic method" to
enumerate sparsely connected hypergraphs asymptotically.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio