Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random band matrices in the delocalized phase, II: Generalized resolvent
  estimates   This is the second part of a three part series abut delocalization for band
matrices. In this paper, we consider a general class of $N\times N$ random band
matrices $H=(H_{ij})$ whose entries are centered random variables, independent
up to a symmetry constraint. We assume that the variances $\mathbb E
|H_{ij}|^2$ form a band matrix with typical band width $1\ll W\ll N$. We
consider the generalized resolvent of $H$ defined as $G(Z):=(H - Z)^{-1}$,
where $Z$ is a deterministic diagonal matrix such that $Z_{ij}=\left(z 1_{1\leq
i \leq W}+\widetilde z 1_{ i > W} \right) \delta_{ij}$, with two distinct
spectral parameters $z\in \mathbb C_+:=\{z\in \mathbb C:{\rm Im} z>0\}$ and
$\widetilde z\in \mathbb C_+\cup \mathbb R$. In this paper, we prove a sharp
bound for the local law of the generalized resolvent $G$ for $W\gg N^{3/4}$.
This bound is a key input for the proof of delocalization and bulk universality
of random band matrices in \cite{PartI}. Our proof depends on a fluctuations
averaging bound on certain averages of polynomials in the resolvent entries,
which will be proved in \cite{PartIII}.

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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: gr-qc