Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectral gap of the path graph in the limit of large volume   In this paper we study the spectral gap of the path graph and illustrate an
interesting effect which has been described recently in the continuous setting.
More explicitly, in the large-volume limit and in the presence of a certain
external potential, it is shown that the spectral gap converges to zero
strictly faster than it does for the free Laplacian. The underlying mechanism
is a combination of the increase in volume and an effective degeneracy of the
ground state in the limiting regime.

23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex