Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge Universality of Beta Ensembles   We prove the edge universality of the beta ensembles for any $\beta\ge 1$,
provided that the limiting spectrum is supported on a single interval, and the
external potential is $\mathscr{C}^4$ and regular. We also prove that the edge
universality holds for generalized Wigner matrices for all symmetry classes.
Moreover, our results allow us to extend bulk universality for beta ensembles
from analytic potentials to potentials in class $\mathscr{C}^4$.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg