Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A probabilistic approach to the Erd\"os-Kac theorem for additive
  functions   We present a new perspective of assessing the rates of convergence to the
Gaussian and Poisson distributions in the Erd\"os-Kac theorem for additive
arithmetic functions $\psi$ of a random integer $J_n$ uniformly distributed
over $\{1,...,n\}$. Our approach is probabilistic, working directly on spaces
of random variables without any use of Fourier analytic methods, and our $\psi$
is more general than those considered in the literature. Our main results are
(i) bounds on the Kolmogorov distance and Wasserstein distance between the
distribution of the normalized $\psi(J_n)$ and the standard Gaussian
distribution, and (ii) bounds on the Kolmogorov distance and total variation
distance between the distribution of $\psi(J_n)$ and a Poisson distribution
under mild additional assumptions on $\psi$. Our results generalize the
existing ones in the literature.

1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys