Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The many faces of the stochastic zeta function   We introduce a framework to study the random entire function $\zeta_\beta$
whose zeros are given by the Sine$_\beta$ process, the bulk limit of beta
ensembles. We present several equivalent characterizations, including an
explicit power series representation built from Brownian motion.
  We study related distributions using stochastic differential equations. Our
function is a uniform limit of characteristic polynomials in the circular beta
ensemble; we give upper bounds on the rate of convergence. Most of our results
are new even for classical values of $\beta$.
  We provide explicit moment formulas for $\zeta$ and its variants, and we show
that the Borodin-Strahov moment formulas hold for all $\beta$ both in the limit
and for circular beta ensembles. We show a uniqueness theorem for $\zeta$ in
the Cartwright class, and deduce some product identities between conjugate
values of $\beta$. The proofs rely on the structure of the Sine$_\beta$
operator to express $\zeta$ in terms of a regularized determinant.

4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph