Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Schreier graphs and expanders   Let the group $G$ act transitively on the finite set $\Omega$, and let $S
\subseteq G$ be closed under taking inverses. The Schreier graph $Sch(G
\circlearrowleft \Omega,S)$ is the graph with vertex set $\Omega$ and edge set
$\{ (\omega,\omega^s) : \omega \in \Omega, s \in S \}$. In this paper, we show
that random Schreier graphs on $C \log|\Omega|$ elements exhibit a (two-sided)
spectral gap with high probability, magnifying a well known theorem of Alon and
Roichman for Cayley graphs. On the other side, depending on the particular
action of $G$ on $\Omega$, we give a lower bound on the number of elements
which are necessary to provide a spectral gap. We use this method to estimate
the spectral gap when $G$ is nilpotent.

17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph