Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coagulation with product kernel and arbitrary initial conditions: Exact
  kinetics within the Marcus-Lushnikov framework   The time evolution of a system of coagulating particles under the product
kernel and arbitrary initial conditions is studied. Using the improved
Marcus-Lushnikov approach, the master equation is solved for the probability
$W(Q,t)$ to find the system in a given mass spectrum
$Q=\{n_1,n_2,\dots,n_g\dots\}$, with $n_g$ being the number of particles of
size $g$. The exact expression for the average number of particles, $\langle
n_g(t)\rangle$, at arbitrary time $t$ is derived and its validity is confirmed
in numerical simulations of several selected initial mass spectra.

10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph