Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the critical points of random matrix characteristic polynomials and
  of the Riemann $\xi$-function   A one-parameter family of point processes describing the distribution of the
critical points of the characteristic polynomial of large random Hermitian
matrices on the scale of mean spacing is investigated. Conditionally on the
Riemann hypothesis and the multiple correlation conjecture, we show that one of
these limiting processes also describes the distribution of the critical points
of the Riemann $\xi$-function on the critical line.
  We prove that each of these processes boasts stronger level repulsion than
the sine process describing the limiting statistics of the eigenvalues: the
probability to find $k$ critical points in a short interval is comparable to
the probability to find $k+1$ eigenvalues there. We also prove a similar
property for the critical points and zeros of the Riemann $\xi$-function,
conditionally on the Riemann hypothesis but not on the multiple correlation
conjecture.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph