Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Class of solvable reaction-diffusion processes on Cayley tree   Considering the most general one-species reaction-diffusion processes on a
Cayley tree, it has been shown that there exist two integrable models. In the
first model, the reactions are the various creation processes, i.e.
$\circ\circ\to\bullet\circ$, $\circ\circ\to\bullet\bullet$ and
$\circ\bullet\to\bullet\bullet$, and in the second model, only the diffusion
process $\bullet\circ\to\circ\bullet$ exists. For the first model, the
probabilities $P_l(m;t)$, of finding $m$ particles on $l$-th shell of Cayley
tree, have been found exactly, and for the second model, the functions
$P_l(1;t)$ have been calculated. It has been shown that these are the only
integrable models, if one restricts himself to $L+1$-shell probabilities
$P(m_0,m_1,...,m_L;t)$s.

6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas