Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of the Spectral Gap for the Interchange Process on Large
  Hypercubes   We consider the interchange process (IP) on the $d$-dimensional, discrete
hypercube of side-length $n$. Specifically, we compare the spectral gap of the
IP to the spectral gap of the random walk (RW) on the same graph. We prove that
the two spectral gaps are asymptotically equivalent, in the limit $n \to
\infty$. This result gives further supporting evidence for a conjecture of
Aldous, that the spectral gap of the IP equals the spectral gap of the RW on
all finite graphs. Our proof is based on an argument invented by Handjani and
Jungreis, who proved Aldous's conjecture for all trees. This also has
implications for the spectral gap of the quantum Heisenberg ferromagnet.

27
The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys