<mods:mods version="3.3" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-3.xsd" xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><mods:titleInfo><mods:title>System of interacting particles with Markovian switching</mods:title></mods:titleInfo><mods:name type="personal"><mods:namePart type="given">А. А.</mods:namePart><mods:namePart type="family">Pogoruі</mods:namePart><mods:role><mods:roleTerm type="text">author</mods:roleTerm></mods:role></mods:name><mods:abstract>Most of the published articles on random motions have been devoted to the study&#13;
of the telegraph process or its generalizations that describe the random motion of a&#13;
single particle in Rn in a Markov or semi-Markov medium. However, up to our best&#13;
knowledge, there are no published papers dealing with the interaction of two or more&#13;
particles which move according to the telegraph processes. In this paper, we construct&#13;
the system of telegraph processes with interactions, which can be interpreted as a&#13;
model of ideal gas. In this model, we investigate the free path times of a family&#13;
of particles, before they are collided with any other particle. We also study the&#13;
distribution of particles, which is described by telegraph processes with hard collisions&#13;
and re&#13;
ecting boundaries, and investigate its limiting properties.</mods:abstract><mods:classification authority="lcc">Mathematical Analysis</mods:classification><mods:originInfo><mods:dateIssued encoding="iso8061">2012</mods:dateIssued></mods:originInfo><mods:genre>Article</mods:genre></mods:mods>