Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the ubiquity of the Cauchy distribution in spectral problems   We consider the distribution of the values at real points of random functions
which belong to the Herglotz-Pick (HP) class of analytic mappings of the upper
half plane into itself. It is shown that under mild stationarity assumptions
the individual values of HP functions with singular spectra have a Cauchy type
distribution. The statement applies to the diagonal matrix elements of random
operators, and holds regardless of the presence or not of level repulsion, i.e.
applies to both random matrix and Poisson-type spectra.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph