# Probability, Random Processes, and Statistical Analysis, by H. Kobayashi, B.L. Mark and W. Turin

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extensions. But in recent years the search has openedup and a number of alternative approaches, such asloop quantum gravity, causal dynamical triangulation,asymptotic safety and numerous others, are starting tobe considered as possible alternatives to this dom-inance. This debate might have been consideredsomewhat abstruse but with recent experiments, forexample those involving Gamma-Ray telescopes ormore detailed maps of the background microwaveradiation (PLANCK), it might soon be possible toactually distinguish amongst some of these alterna-tives predictions. Now is therefore a good time toweigh up these differing approaches and see what eachcan bring to the debate.

This book, significantly rewritten and updated inthis latest edition, is without doubt an excellent sourceto gain an overall understanding of these developmentsbefore one might consider specialising on some specifictopic within this panoply of approaches. Amongst thetopics included are Hamiltonian and covariant meth-ods, loop formulism and quantum cosmological aspectsas well as a chapter on string theory itself. Morefundamental questions are addressed such as if quan-tum gravity is strictly necessary. Also the somewhatobscure notion of how to quantise and obtain time froma formally reparametrisation invariant theory such asgeneral relativity; and the role of quantum decoherencein possibly explaining how classical behaviour actuallydevelops in an expanding universe. The authors ownwork on the quantisation of black holes and collapsingdust shells is extensively presented. Overall the pre-sentation is balanced and without any exaggeratedclaims for any one particular approach.

At times the manuscript is rather concise andrequires a careful reading. For starting students Iwould also recommend the lectures on QuantumGravity by Professor Renate Loll, that closely followsections of an earlier edition of this book, especially forreaders attempting to learn without formal lectures:available online from the Perimeter Institute ofTheoretical Physics (http://pirsa.org). More estab-lished researchers will also find much here to con-template and ponder.

Although there has been much progress during thepast few years there are still plenty of fundamentalissues that are still unresolved. In the application tocosmology: whether there is an initial low entropy statethat might give inflationary expansion or the possibi-lity of a big bounce that might connect the universe toa preceding collapsing phase are the two mostlyconsidered paradigms but no doubt other ideas willbe developed. Hopefully readers of this title will bemotivated to delve deeper into some of these intriguingquestions. But in the meantime, albeit with somediligent work, they should gain sufficient grounding

here to begin the journey armed with a good overallgrasp of the subject.

David H. CouleUniversity of Portsmouthdavid.coule@port.ac.uk

2012, David H. Coulehttp://dx.doi.org/10.1080/00107514.2012.737858

Probability, Random Processes, and Statistical Analy-sis, by H. Kobayashi, B.L. Mark and W. Turin,Cambridge, Cambridge University Press, 2011, 812pp., 45.00 (hardback), ISBN 978-0-52-189544-6.Scope: textbook. Level: undergraduate students, re-searchers, teachers.

The Theory of Probability is the area which was bothcreated by and deals with the mathematical descriptionof random/stochastic events both in nature and in life(and perhaps also in History), as well as with the effortto predict them.

The work is a treatment of the fascinating and well-known field of Probability and Statistics which is ripewith applications and their respective procedures. Weshould begin by borrowing a phrase from the penulti-matework in the field,A. Papoulis book onProbability,in which he writes (p. 3): probability, like any physicaltheory, is related to physical phenomena only in inexactterms. Nevertheless, the theory is an exact disciplinedeveloped logically from clearly defined axioms, andwhen it is applied to real problems, it works.

The core of this work and its main theme is, as thecontributors themselves state, the interplay betweenprobability theory and statistical analysis. They alsoclaim that the work breaks new ground with itspresentation of the relationship between abstractprobability theory and real statistical data, as well asgraphical representations. It is worth noting at theoutset the central axis of the work: classical probabilitytheory modern probability theory random processes statistical analysis.

The ultimate applications of this work are focusedprimarily on the field of Informatics. Processes andfields of probability are developed that relate to areasof computer science, and special mention is made ofapplications in various areas of computers, such as,e.g. the Internet and the traffic routed therein,bioinformatics, etc.

The subject matter is viewed through the lens of themore up-to-date approach to probability theory(Kolmogorov etc.) without of course overlooking themore conventional approaches, i.e. frequentist statis-tics and Bayesian statistics.

Contemporary Physics 533

http://pirsa.org)

Central to the theory of probability, as in thiswork, is central limit theorem (CLT) (as well as theLaw of large numbers), which assures us that(absolute) randomness does not exist in the world.Special interest and elaboration is given also toMarkov processes and Monte Carlo techniques, whichis particularly apropos here.

The following observation is especially noteworthyand surprising: generalised probability processes areapplied to a variety of highly divergent disciplines (e.g.from computer science and the Internet on the onehand, to econometrics on the other). This creates aunified tree-like distribution of things (intangibles, i.e.processes and theories, and materials, i.e. applicationsand results) in the Universe. In this distribution, thegeneralised processes are assumed to be on the upperradical level(s), while their applications in diverse fieldsand areas are located on the subsequent levels. Thisobservation, of course, also applies to other areas ofscience beyond probability, and it is the wonderful andperhaps even paradoxical commonplace which mancan observe both in his life and in the nature aroundhim: namely, the existence of common applicable andvalid prototypes dispersed through the whole world,through its things and processes.

The contributors prefer to include the most well-known issues in the subject under consideration, and asmany and as wide a variety as possible of relatedsubjects which fall within its purview. The breadth theymanage to cover is, indeed, remarkable. It is quite clearthat the contributors are attempting to broaden thescope of the works scientific content in order to targeta wide range of sciences (for instance, physics, finance,chemistry). However, the primary fields of interest andapplications are Information & Computer Sciences(e.g. signal processing, queuing theory, machinelearning, econometrics, etc.).

Finally, the textbook is written in the usualframework with a pleasant and uncomplicated style,suitable for teaching students, as well as for use as anintroductory handbook and guide to the field.

Nikolaos E. MyridisAristotle University of Thessaloniki

nmyridis@theo.auth.gr 2012, Nikolaos E. Myridis

http://dx.doi.org/10.1080/00107514.2012.737860

Rotating Flow, by Peter Childs, Oxford, Elsevier, 2010,416 pp., 59.99 (hardback), ISBN 978-0-12-382098-3.Scope: review. Level: postgraduates, scientists, engineers.

The book consists of eight chapters and blendstheoretical, modelling and experimental aspects of

rotating flow which are crucial for nature andmachinery applications. In the book, real engineeringapplications and natural examples are provided anddesign-oriented correlations of bulk parameters arefrequently given throughout the book.

The first chapter introduces the reader to rotatingflows through ample examples. Chapter 2 is devotedto the derivation of the governing equations (mo-mentum and continuity equations) of rotating flow.The same chapter introduces dimensional analysisand the similarity concept. The basic principle ofvortices is studied in the third chapter with anintroduction to their mathematical formulations andillustrative examples. Chapter 4 covers rotating discsystems, and considers laminar and turbulent flowsover a free single disc as well as a rotating fluid abovea stationary disc. As an extension of Chapter 4,Chapter 5 discusses the rotorstator cavity flow. Flowover rotating curved surfaces such as cylinders, annuliand spheres are studied in Chapter 6. Flow instabil-ities of the rotating flow are examined using Rayleighcriterion. Journal-bearing processes involving bound-ary, mixed-film and full-film hydrodynamic lubricationsare also discussed in depth. Chapter 7 covers rotatingcavity flow that forms between co-rotating co-axialdiscs with an outer shroud, and investigates theboundary layer approximation of the rotating cavityflow. The last chapter discusses the atmospheric andoceanic circulations that are affected by earth rotationand motion. This chapter provides integrated informa-tion about atmospheric and oceanic dynamics.

The main emphasis of the book is mathematicalmodelling with less attention to the numerical methodsthat are necessary for computational fluid dynamicssimulations.

I recommend this book for those graduate studentswho want a thorough theoretical and modellingfoundation in the topic of rotating flow.

M.F. El-AminKing Abdullah University of Science and Technology

(KAUST)mohamed.elamin@kaust.edu.sa

2012, M.F. El-Aminhttp://dx.doi.org/10.1080/00107514.2012.739647

Disordered Semiconductors: Physics and Applications,by Anatoly Popov, Singapore, Pan StanfordPublishing, 2010, 400 pp., 114.95 (paperback), ISBN978-9-81-424176-2. Scope: review. Level: advancedundergraduates.

The concept of translational symmetry and long-range order in arrangement of atoms in any single

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