Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On fluctuations of global and mesoscopic linear eigenvalue statistics of
  generalized Wigner matrices   We consider an $N$ by $N$ real or complex generalized Wigner matrix $H_N$,
whose entries are independent centered random variables with uniformly bounded
moments. We assume that the variance profile, $s_{ij}:=\mathbb{E} |H_{ij}|^2$,
satisfies $\sum_{i=1}^Ns_{ij}=1$, for all $1 \leq j \leq N$ and $c^{-1} \leq N
s_{ij} \leq c$ for all $ 1 \leq i,j \leq N$ with some constant $c \geq 1$. We
establish Gaussian fluctuations for the linear eigenvalue statistics of $H_N$
on global scales, as well as on all mesoscopic scales up to the spectral edges,
with the expectation and variance formulated in terms of the variance profile.
We subsequently obtain the universal mesoscopic central limit theorems for the
linear eigenvalue statistics inside the bulk and at the edges respectively.

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The categories of this paper are: cs
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph