Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalues of even very nice Toeplitz matrices can be unexpectedly
  erratic   It was shown in a series of recent publications that the eigenvalues of
$n\times n$ Toeplitz matrices generated by so-called simple-loop symbols admit
certain regular asymptotic expansions into negative powers of $n+1$. On the
other hand, recently two of the authors considered the pentadiagonal Toeplitz
matrices generated by the symbol $g(x)=(2\sin(x/2))^4$, which does not satisfy
the simple-loop conditions, and derived asymptotic expansions of a more
complicated form. We here use these results to show that the eigenvalues of the
pentadiagonal Toeplitz matrices do not admit the expected regular asymptotic
expansion. This also delivers a counter-example to a conjecture by Ekstr\"{o}m,
Garoni, and Serra-Capizzano and reveals that the simple-loop condition is
essential for the existence of the regular asymptotic expansion.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg