Table Of Contentedited
)brust
a
Ya.G.Sir
ADVANCES IN PROBABILITY AND RELATED TOPICS VOLUME 6
Series Editor: Peter'Ney
MULTICOMPONENT
RANDOM SYSTEMS
ADVANCES IN PROBABILITY and Related Topics
Editor: Peter Ney
Department of Mathematics
University of Wisconsin-Madison
Madison, Wisconsin
Vols. 1 and 2 Advances in Probability and Related Topics, edited by Peter Ney
Vol.3 Advances in Probability and Related Topics, edited by Peter Ney and
Sidney Port
Vol. 4 Probability on Banach Spaces, edited by James Kuelbs
Vol. 5 Branching Processes, edited by Anatole Joffe and Peter Ney
Vol. 6 Multicomponent Random Systems, edited by R. L. Dobrushin and
Ya. G. Sinai
Other volumes in preparation
MULTICOMPONENT
RANDOM SYSTEMS
edited by
R.L. Dobiushin and Ya. G. Sinol
Institute for Inionnation Transmission Problems
and Landau Institute oí Theoretical Physics
Academy oí Sciences
Moscow, USSR
contributing editor
D. Giiifeath
series editor
Peter Ney
MARCEL DEKKER, Inc. New York and Basel
Library of Congress Cataloging in Publication Data
Main entry under title:
Multicomponent random systems.
(Advances in probability and related topics ;
vol. 6)
Originally published in Russian.
I. Stochastic processes. 2. Stochastic
systems. I. Dobrushin, R. L.,
II. Sinai, IAkov Grigor’evich,
III. Griffeath, David. IV. Series.
QA273.A1A4 vol. 6 [QA274] 519.2s [519.2]
ISBN 0-8247-6831-0 80-17688
COPYRIGHT © 1980 by MARCEL DEKKER, INC. ALL RIGHTS RESERVED
Neither this book nor any part may be reproduced or transmitted in any form or by any
means, electronic or medhanical, including photocopying, microfilming, and recording,
or by any information storage or retrieval system, without permission m writing
from the publisher.
MARCEL DEKKER, INC.
270 Madison Avenue, New York, New York 10016
Current printing (last digit):
10 987654321
PRINTED IN THE UNITED STATES OF AMERICA
INTRODUCTION ТО THE SERIES
Advances in Probability and Related Topics was founded in 1970 to provide a flexible
medium for publication of work in probability theory and related areas. The idea was
to encourage lucid exposition of topics of current interest, while giving authors greater
flexibility on the inclusion of original and expository material and on the lengths of
articles than might be available in standard journak. There has not been any particular
focxis of subject matter, other than its relevance to probability theory.
During the past decade, a variety of series have evolved which now offer the op-
portimity for this kind of publication. We have therefore decided to modify our for
mat to focus the attention of each volume on a single unified subarea of probability
theory, whüe retaining flexibility in the format of individual articles.
To this end. Volume 4 focused on Probability on Banach Spaces, Volume 5 on
Branching Processes, while the present volume is on Multicomponent Random Systems.
We intend to maintain flexible editorial arrangements. The editors for the vari
ous volumes will in general be experts in a special area of probability theory and will
be responsible for the contents of their particular volume. People who might be inter
ested in editing such a volume are invited to contact the Series Editor.
Peter Ney
NOTE FROM THE EDITORS
The contributions to this volume are the work of mathematicians connected with
the Institute for Information Transmission Problems in Moscow. The original versions
were in Russian. Preliminary translations into English were provided by the authors,
but in many cases there remained an extensive job of completing the translations.
This was done entirely on a volimteer basis by colleagues at American universities who
felt that this project was of value. Our heartiest thanks go out to the following people
for their assistance in this connection: R. Arratia, M. Bramson, J. Chover, D. Daw
son, S. Goldstein, L. Gray, R. Holley, H. Kesten, J. Lebowitz, S. Sawyer, and F. Spit
zer. The original suggestion and impetus for the publication of this volume came from
Frank Spitzer.
A casual perusal of the pages in the volume will convince the reader that the form
ulas and notation in some papers are xmusually complex. This, together with the con
siderable separation in space time of the Soviet authors, volunteer translators, local
editors, and the typist, made the logistics of producing this volume imusually compli
cated. The difficult typing task, done from copy of variable quality, was superbly
carried out by Mrs. Grace Krewson. We extend our sincere thanks to her, and to Mrs.
Emmy Alford for a variety of editorial assistance.
D. Griffeath
Peter Ney
PREFACE
Over the last decade there has taken shape and, we can say, ripened a new inter
disciplinary scientific field--a theory of multicomponent random systems. The main
object of study here is multidimensional systems comprising a large number of homo
geneous locally interacting components. These components may be of different real
nature depending on the field of their application. In physical applications these are
atoms in points of crystal lattices; in cybernetic applications, interacting finite-state
automata, logic-informational elements, and queue systems; in biological applications,
cells, neurons, etc.. It is believed that the range of the real phenomena, the mathema
tical description of which naturally leads to the models of the discussed type, is ex
tremely wide.
As a branch of applied mathmatics, the theory of multicomponent random systems
came into being on the intersection of the theory of probability, statistical physics,
information theory, mathematical biology. Some of its basic notions, e.g., the notion
of the Markov process with interaction was created in parallel by representatives of
аД these fields of science. But the most important proved to be the influence of stat
istical physics, apparently because the scientific experience accumulated by this field is
incomparably deeper than that of younger sciences. The decisive factor was the devel
opment of mathematically rigourous statistical physics. At first its evolution was mo
tivated by the desire to substantiate logically the fundamental physical notions, how-
VU
