Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Independent sets in random subgraphs of the hypercube   Let $Q_{d,p}$ be the random subgraph of the $d$-dimensional hypercube
$\{0,1\}^d$, where each edge is retained independently with probability $p$. We
study the asymptotic number of independent sets in $Q_{d,p}$ as $d \to \infty$
for a wide range of parameters $p$, including values of $p$ tending to zero as
fast as $\frac{C\log d}{d^{1/3}}$, constant values of $p$, and values of $p$
tending to one. The results extend to the hardcore model on $Q_{d,p}$, and are
obtained by studying the closely related antiferromagnetic Ising model on the
hypercube, which can be viewed as a positive-temperature hardcore model on the
hypercube. These results generalize previous results by Galvin, Jenssen and
Perkins on the hard-core model on the hypercube, corresponding to the case
$p=1$, which extended Korshunov and Sapozhenko's classical result on the
asymptotic number of independent sets in the hypercube.

21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int