
Monte Carlo Methods
Description
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The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks.
The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter.
This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
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Persons
Paula A. Whitlock is Professor of Computer and Information Sciences at Brooklyn College, the City University of New York. She received her BS at the State University of New York at Stony Brook and her PhD at Wayne State University. For many years, she was a research scientistat the Courant Institute of Mathematical Sciences, New York University. Her research interests include the development of Monte Carlo methods and their application to the study of condensed matter systems. Professor Whitlock is also interested in the development of applications in distributed computing.
Content
1 What is Monte Carlo?
2 A Bit of Probability
3 Sampling Random Variables
4 Monte Carlo Evaluation of Finite-Dimensional Integrals
5 Random Walks, Integral Equations, and Variance Reduction
6 Simulations of Stochastic Systems: Radiation Transport
7 Statistical Physics
8 Quantum Monte Carlo
9 Pseudorandom Numbers
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