Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: System of interacting particles with Markovian switching   Most of the published articles on random motions have been devoted to the
study of the telegraph process or its generalizations that describe the random
motion in $R^n$ of a single particle in a Markov or semi-Markov medium.
However, up to our best knowledge there are no published papers dealing with
the interaction of two or more particles which move according to the telegraph
processes. In this paper, we construct the system of telegraph processes with
interactions, which can be interpreted as a model of ideal gas. In this model,
we investigate the free path times of a family of particles before they are
collided with any other particle. We also study the distribution of particles,
which described by telegraph processes with hard collisions and reflecting
boundaries, and investigate its limiting properties.

25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ