Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replica-symmetric approach to the typical eigenvalue fluctuations of
  Gaussian random matrices   We discuss an approach to compute the first and second moments of the number
of eigenvalues $I_N$ that lie in an arbitrary interval of the real line for $N
\times N$ Gaussian random matrices. The method combines the standard
replica-symmetric theory with a perturbative expansion of the saddle-point
action up to $O(1/N)$ ($N \gg 1$), leading to the correct logarithmic scaling
of the variance $\langle I_{N}^{2} \rangle - \langle I_N \rangle^2 = O(\ln N)$
as well as to an analytical expression for the $O(1/N)$ correction to the
average $\langle I_N \rangle/N$. Standard results for the number variance at
the local scaling regime are recovered in the limit of a vanishing interval.
The limitations of the replica-symmetric method are unveiled by comparing our
results with those derived through exact methods. The present work represents
an important step to study the fluctuations of $I_N$ in non-invariant random
matrix ensembles, where the joint distribution of eigenvalues is not known.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph