John Gubner
Probability and Random Processes for Electrical and Computer
Engineers
Hardback (ISBN-13: 9780521864701 | ISBN-10: 0521864704)
available from June 2006
Courses: Probability and Random Processes (as a primary text) -
graduate level - Electrical and Computer Engineering Departments.
Wireless Communications (as a background text in probability) -
graduate level - Electrical and Computer Engineering Departments.
Also suitable for advanced undergraduates.
The theory of probability has important applications for computer
and electrical engineers as a tool to explain, model, analyse and
design the technology they develop. Consequently, a course in
probability and random processes is a prerequisite for further
study in communications or signal processing. Gubner presents a
primary text that progresses from advanced undergraduate level,
assuming a modest knowledge of probability, through to the more
complex topics suitable for graduates, including random vectors,
Gaussian random vectors, random processes and Markov chains.
Describing tools and results that are used extensively in the
field, this is more than a textbook: it is also a valuable
reference for researchers working in communications, signal
processing, and computer network traffic analysis. With chapter
outlines, over 300 worked examples, some 800 problems and
sections for exam preparation, this is an essential companion for
advanced undergraduate and graduate students.
* Each chapter contains a eNotesf section at the end to
discuss the more techincal points of theory
* There are worked examples throughout the main text, accompanied
by homework problems (800 in total) and exam preparation at the
end of each chapter: a number of examples and problems use MATLAB
* The book is structured such that instructors can target the
level (undergraduate or graduate) of the course to suit the
background of the students
Contents
Chapter dependencies; Preface; 1. Introduction to probability; 2.
Introduction to discrete random variables; 3. More about discrete
random variables; 4. Continuous random variables; 5. Cumulative
distribution functions and their applications; 6. Statistics; 7.
Bivariate random variables; 8. Introduction to random vectors; 9.
Gaussian random vectors; 10. Introduction to random processes; 11.
Advanced concepts in random processes; 12. Introduction to Markov
chains; 13. Mean convergence and applications; 14. Other modes of
convergence; 15. Self similarity and long-range dependence;
Bibliography; Index.
Jean Bertoin
Random Fragmentation and Coagulation Processes
Series: Cambridge Studies in Advanced Mathematics (No. 102)
Hardback (ISBN-13: 9780521867283 | ISBN-10: 0521867282)
available from July 2006
Fragmentation and coagulation are two natural phenomena that can
be observed in many sciences and at a great variety of scales -
from, for example, DNA fragmentation to formation of planets by
accretion. This book, by the author of the acclaimed Levy
Processes, is the first comprehensive theoretical account of
mathematical models for situations where either phenomenon occurs
randomly and repeatedly as time passes. This self-contained
treatment develops the models in a way that makes recent
developments in the field accessible. Each chapter ends with a
comments section in which important aspects not discussed in the
main part of the text (often because the discussion would have
been too technical and/or lengthy) are addressed and precise
references are given. Written for readers with a solid background
in probability, its careful exposition allows graduate students,
as well as working mathematicians, to approach the material with
confidence.
* Author is the world-leading expert on the field and a great
expositor
* The first book on an important class of stochastic models
* Wide-ranging areas of application - computer science, physics,
geophysics, biology and more
Contents
Introduction; 1. Self-similar fragmentation chains; 2. Random
partitions; 3. Exchangeable fragmentations; 4. Exchangeable
coalescents; 5. Asymptotic regimes in stochastic coalescence;
References; List of symbols; Index.
Alexandru Nica / University of Waterloo, Ontario
Roland Speicher / Queen's University, Ontario
Lectures on the Combinatorics of Free Probability
Series: London Mathematical Society Lecture Note Series (No.
335)
Paperback (ISBN-13: 9780521858526 | ISBN-10: 0521858526)
available from September 2006
Free Probability Theory studies a special class of enoncommutativefrandom
variables, which appear in the context of operators on Hilbert
spaces and in one of the large random matrices. Since its
emergence in the 1980s, free probability has evolved into an
established field of mathematics with strong connections to other
mathematical areas, such as operator algebras, classical
probability theory, random matrices, combinatorics,
representation theory of symmetric groups. Free probability also
connects to more applied scientific fields, such as wireless
communication in electrical engineering. This book is the first
to give a self-contained and comprehensive introduction to free
probability theory which has its main focus on the combinatorial
aspects. The volume is designed so that it can be used as a text
for an introductory course (on an advanced undergraduate or
beginning graduate level), and is also well-suited for the
individual study of free probability.
* Presents the state of the art of the combinatorial facet of
free probability
* Gives a friendly and self-contained introduction to the general
field of free probability
* Written in a style which makes it ideal for use in the
presentation of a graduate level course
Contents
Part I. Basic Concepts: 1. Non-commutative probability spaces and
distributions; 2. A case study of non-normal distribution; 3. C*-probability
spaces; 4. Non-commutative joint distributions; 5. Definition and
basic properties of free independence; 6. Free product of *-probability
spaces; 7. Free product of C*-probability spaces; Part II.
Cumulants: 8. Motivation: free central limit theorem; 9. Basic
combinatorics I: non-crossing partitions; 10. Basic Combinatorics
II: Mobius inversion; 11. Free cumulants: definition and basic
properties; 12. Sums of free random variables; 13. More about
limit theorems and infinitely divisible distributions; 14.
Products of free random variables; 15. R-diagonal elements; Part
III. Transforms and Models: 16. The R-transform; 17. The
operation of boxed convolution; 18. More on the 1-dimensional
boxed convolution; 19. The free commutator; 20. R-cyclic
matrices; 21. The full Fock space model for the R-transform; 22.
Gaussian Random Matrices; 23. Unitary Random Matrices; Notes and
Comments; Bibliography; Index.
Jos W. R. Twisk
VU Medical Canter, Amsterdam
Applied Multilevel Analysis
A Practical Guide for Medical Researchers
Series: Practical Guides to Biostatistics and Epidemiology
Hardback (ISBN-13: 9780521849753 | ISBN-10: 0521849756)
Paperback (ISBN-13: 9780521614986 | ISBN-10: 0521614988)
available from April 2006
This is a practical introduction to multilevel analysis suitable
for all those doing research. Most books on multilevel analysis
are written by statisticians, and they focus on the mathematical
background. These books are difficult for non-mathematical
researchers. In contrast, this volume provides an accessible
account on the application of multilevel analysis in research. It
addresses the practical issues that confront those undertaking
research and wanting to find the correct answers to research
questions. This book is written for non-mathematical researchers
and it explains when and how to use multilevel analysis. Many
worked examples, with computer output, are given to illustrate
and explain this subject. Datasets of the examples are available
on the internet, so the reader can reanalyse the data. This
approach will help to bridge the conceptual and communication gap
that exists between those undertaking research and statisticians.
* Non-mathematical approach
* Computer output of all examples
* Comparison between software packages
Contents
Preface; 1. Introduction; 2. Basic principles behind multilevel
analysis; 3. What do we gain by applying multilevel analysis?; 4.
Multilevel analysis with different outcome variables; 5.
Multilevel modelling; 6. Multilevel analysis in longitudinal
studies; 7. Multivariate multilevel analysis; 8. Sample size
calculations in multilevel studies; 9. Software for multilevel
analysis; References; Index.