Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative Marcinkiewicz's theorem and central limit theorems:
  applications to spin systems and point processes   The classical Marcinkiewicz theorem states that if an entire characteristic
function $\Psi$ of a non-degenerate real-valued random variable $X$ is of the
form $\exp(P(u))$ for some polynomial $P$, then $X$ has to be a Gaussian. In
this work, we obtain a broad, quantitative extension of this framework in
several directions, establish central limit theorems (CLTs) with explicit rates
of convergence, and demonstrate Gaussian fluctuations in continuous spin
systems and general classes of point processes. In particular, we obtain
quantitative decay estimates on the Kolmogorov-Smirnov distance between $X$ and
a Gaussian under the condition that $\Psi$ does not vanish only on a bounded
disk. This leads to quantitative CLTs applicable to very general and possibly
strongly dependent random systems. In spite of the general applicability, our
rates for the CLT match the classic Berry-Esseen bounds for independent sums up
to a log factor. We implement this programme for two important classes of
models in probability and statistical physics. First, we extend to the setting
of continuous spins a popular paradigm for obtaining CLTs for discrete spin
systems that is based on the theory of Lee-Yang zeros, focussing in particular
on the XY model, Heisenberg ferromagnets and generalised Ising models.
Secondly, we establish Gaussian fluctuations for linear statistics of so-called
$\alpha$-determinantal processes for $\alpha \in \mathbb{R}$ (including the
usual determinantal, Poisson and permanental processes) under very general
conditions, including in particular higher dimensional settings where
structural alternatives such as random matrix techniques are not available. Our
applications demonstrate the significance of having to control the
characteristic function only on a (small) disk, and lead to CLTs which, to the
best of our knowledge, are not known in generality.

15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat