Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral Independence in High-Dimensional Expanders and Applications to
  the Hardcore Model   We say a probability distribution $\mu$ is spectrally independent if an
associated correlation matrix has a bounded largest eigenvalue for the
distribution and all of its conditional distributions. We prove that if $\mu$
is spectrally independent, then the corresponding high dimensional simplicial
complex is a local spectral expander. Using a line of recent works on mixing
time of high dimensional walks on simplicial complexes
\cite{KM17,DK17,KO18,AL19}, this implies that the corresponding Glauber
dynamics mixes rapidly and generates (approximate) samples from $\mu$.
  As an application, we show that natural Glauber dynamics mixes rapidly (in
polynomial time) to generate a random independent set from the hardcore model
up to the uniqueness threshold. This improves the quasi-polynomial running time
of Weitz's deterministic correlation decay algorithm \cite{Wei06} for
estimating the hardcore partition function, also answering a long-standing open
problem of mixing time of Glauber dynamics \cite{LV97,LV99,DG00,Vig01,EHSVY16}.

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The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol