Expected publication date is April 16, 2005
Description
Theoretical physicists have predicted that the scaling limits of
many two-dimensional lattice models in statistical physics are in
some sense conformally invariant. This belief has allowed
physicists to predict many quantities for these critical systems.
The nature of these scaling limits has recently been described
precisely by using one well-known tool, Brownian motion, and a
new construction, the Schramm-Loewner evolution (SLE).
This book is an introduction to the conformally invariant
processes that appear as scaling limits. The following topics are
covered: stochastic integration; complex Brownian motion and
measures derived from Brownian motion; conformal mappings and
univalent functions; the Loewner differential equation and
Loewner chains; the Schramm-Loewner evolution (SLE), which is a
Loewner chain with a Brownian motion input; and applications to
intersection exponents for Brownian motion. The prerequisites are
first-year graduate courses in real analysis, complex analysis,
and probability. The book is suitable for graduate students and
research mathematicians interested in random processes and their
applications in theoretical physics.
Contents
Some discrete processes
Stochastic calculus
Complex Brownian motion
Conformal mappings
Loewner differential equation
Brownian measures on paths
Schramm-Loewner evolution
More results about SLE
Brownian intersection exponent
Restriction measures
Hausdorff dimension
Hypergeometric functions
Reflecting Brownian motion
Bibliography
Index
Index of symbols
Details:
Series: Mathematical Surveys and Monographs, Volume: 114
Publication Year: 2005
ISBN: 0-8218-3677-3
Paging: 242 pp.
Binding: Hardcover
Enhancements based on newly released Maple 9.5
Backwards compatible for all Maple versions
More detail in its step-by-step examples
Reviews
"Overall, I found the book very nice to read and easy to
follow. All major aspects of Maple that a novice to intermediate
user would come across are covered."
Laurent Bernard, Maplesoft, Inc.
"The book is eminently readable with a good narrative style
and a good blend of didactic exposition followed by the relevant
Maple commands. What is especially instructive is the numerous
times alternative ways are used to produce equivalent answers
showing the versatility of Maple and leaving the choice of method
to the reader who attempts similar problems." David
Hodgkinson, University of Liverpool
Contents
Ch1. Getting Started: Introduction to Maple. Getting Started With
Maple. 5 Basic Rules of Maple Syntax, Loading Packages. Getting
Help from Maple.
Ch. 2 Numbers, Expressions, and Functions: Numerical
Calculations, Built-In Constants, Built-In Functions. Expressions
and Functions: Linear Algebra, Graphing Functions, Expressions,
and Equations, Solving Equations and Inequalities.
Ch. 3 Calculus: Limits. Differential Calculus. Integral Calculus.
Series.
Multi-Variable Calculus.
Ch. 4 Introduction to Lists and Tables: Lists and List
Operations, Manipulating Lists: More on op and map, Mathematics
of Finance. Other Applications.
Ch 5. Matrices and Vectors: Introduction to Matrices and Vectors,
Linear Systems of Equations. Selected Topics from Linear Algebra.
Maxima and Minima Using Linear Programming. Selected Topics from
Vector Calculus.
Ch. 6 Differential Equations: First-Order Ordinary Differential
Equations, Second-Order Linear Equations, Higher-Order Linear
Equations, Systems of Equations, Some Partial Differential
Equations.
Readership: Students and practitioners of mathematics,
engineering, and statistics from the most elementary to the most
advanced levels will find that the range of topics covered
addresses their needs.
ISBN: 0-12-088526-3 Paperback
Line Illustrations: 208
Measurements: 7 1/2 X 9 1/4 in Pages: 704
Publication Date: 1 April 2005
Series: Progress in Mathematics,
2005, Hardcover
ISBN: 3-7643-4299-4
About this book
This monograph examines the boundary behavior of holomorphic
functions in several complex variables. Moving beyond the early
ideas of Fatou and others, Koranyi and then Stein in the late
1960s and early 1970s deepened the study of Fatou-type theorems
in several complex variables, showing that in a general context,
approach regions of a shape dramatically larger than "non-tangential"
will give rise to a Fatou-type theorem. These have become known
as the admissible regions of Koranyi and Stein. It turns out,
however, that the admissible approach regions are only optimal on
strongly pseudoconvex domains. Considerable effort has been made
in the last 20 years to adapt Fatou theory, and the approach
regions in particular, to the Levi geometry of a given domain in
multidimensional complex space. The work of Di Biase in the late
1990s is devoted to the Nagel--Stein phenomenon, describing a
more general notion of approach region that supersedes the
classical ideas of non-tangential and admissible. Krantz's work
"Function Theory of Several Complex Variables" (2000),
still the only introduction to the subject, focuses on methods
based on maximal function estimates. To date, "the main open
problem, which is the special focus of this book, is the issue of
determining the {\it optimal natural approach regions} for the
almost everywhere convergence to the boundary of certain smoothly
bounded pseudoconvex domains." This book provides the proper
framework for the eventual solution of the main problem. This
work gives an updated, comprehensive, and self-contained
exposition of many results that have never appeared in book form.
Starting with foundational material, i.e., from the unit disc in
one complex variable, the reader is lead to the latest
discoveries in higher dimensions. New results in boundary value
issues of holomorphic functions are examined, which in turn point
to new open problems. The book may be used by analysts for
individual study or by graduate students.
Table of contents
Prelude: Starting from the Unit Disc * Preliminary Results * The
Geometric Context * Finite Type Conditions * Approach Regions and
Finite Type * Radial Convergence and Lindelof Theorems * Theorems
of Littlewood Type in C^n * The Natural Approach Regions in C^n *
Bibliography * Index
Paperback ISBN 0521619475
Not yet published - available from March 2005
This book examines in detail two of the fundamental questions
raised by quantum mechanics. Is the world indeterministic? Are
there connections between spatially separated objects? In the
first part of the book after outlining the formalism of quantum
mechanics and introducing the measurement problem, the author
examines several interpretations, focusing on how each proposes
to solve the measurement problem and on how each treats
probability. In the second part, the author argues that there can
be non-trivial relationships between probability (specifically,
determinism and indeterminism) and non-locality in an
interpretation of quantum mechanics. The author then re-examines
some of the interpretations of part one of the book in the light
of this argument, and considers how they are with regard to
locality and Lorentz invariance. One of the important lessons
that comes out of this discussion is that any examination of
locality, and of the relationship between quantum mechanics and
the theory of relativity, should be undertaken in the context of
a detailed interpretation of quantum mechanics. The book will
appeal to anyone with an interest in the interpretation of
quantum mechanics, including researchers in the philosophy of
physics and theoretical physics, as well as graduate students in
those fields.
Contents
Preface; Acknowledgement; Part I. Quantum Chance: 1. Quantum
probability and the problem of interpretation; 2. Orthodox
theories; 3. No-collapse theories; 4. Modal interpretations; 5.
The Bohm theory; Part II. Quantum Non-locality: 6. Non-locality I:
Non-dynamical models of the EPR-Bohm experiment; 7. Non-locality
II: Dynamical models of the EPR-Bohm experiment; 8. Non-locality
and special relativity; 9. Probability and non-locality; Notes;
References; Index.
Hardback ISBN 0521842387
Not yet published - available from June 2005
This new and updated edition deals with all aspects of Monte
Carlo simulation of complex physical systems encountered in
condensed-matter physics, statistical mechanics, and related
fields. After briefly recalling essential background in
statistical mechanics and probability theory, it gives a succinct
overview of simple sampling methods. The concepts behind the
simulation algorithms are explained comprehensively, as are the
techniques for efficient evaluation of system configurations
generated by simulation. It contains many applications, examples,
and exercises to help the reader and provides many new references
to more specialized literature. This edition includes a brief
overview of other methods of computer simulation and an outlook
for the use of Monte Carlo simulations in disciplines beyond
physics. This is an excellent guide for graduate students and
researchers who use computer simulations in their research. It
can be used as a textbook for graduate courses on computer
simulations in physics and related disciplines.
Contents
1. Introduction; 2. Some necessary background; 3. Simple sampling
Monte Carlo methods; 4. Importance sampling Monte Carlo methods;
5. More on importance sampling Monte Carlo method for lattice
systems; 6. Off-lattice models; 7. Reweighting methods; 8.
Quantum Monte Carlo methods; 9. Monte Carlo Renormalization Group
methods; 10. Non-equilibrium and irreversible processes; 11.
Lattice gauge models: a brief introduction; 12. A brief review of
other methods of computer simulation; 13. Monte Carlo methods
outside of physics; 14. Outlook.
Review
From the first edition: eThis book will serve as a useful
introduction to those entering the field, while for those already
versed in the subject it provides a timely survey of what has
been achieved.f Journal of Statistical Physics