Elements of the Random Walk: An introduction for Advanced Students and Researchers

by Joseph Rudnick, George Gaspari

Overview

Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. This book is an introduction to some of the most powerful and general techniques used in the application of these ideas. Its self-contained text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

Product Details

ISBN-13:	9780521828918
Publisher:	Cambridge University Press
Publication date:	03/04/2004
Pages:	346
Product dimensions:	6.69(w) x 9.61(h) x 0.83(d)

About the Author

Joseph Rudnick earned his PhD in
1970. He has held faculty positions at Tufts University and the University of California, Santa Cruz. He has held a visiting position at Harvard University. He is currently a Professor in the Department of Physics and Astronomy at the University of California, Los Angeles.

George Gaspari has been a Research Associate at the University of Rochester and has held visiting positions at the University of Bristol, UK, Stanford University and the University of California, Los Angeles. He has been a Sloan Foundation Fellow.

Table of Contents

Preface; 1. Introduction to techniques; 2. Generating functions I; 3. Generating functions II: recurrence, sites visited, and the role of dimensionality; 4. Boundary conditions, steady state, and the electrostatic analogy; 5. Variations on the random walk; 6. The shape of a random walk; 7. Path integrals and self-avoidance; 8. Properties of the random walk: introduction to scaling; 9. Scaling of walks and critical phenomena; 10. Walks and the O(n) model: mean field theory and spin waves; 11. Scaling, fractals, and renormalization; 12. More on the renormalization group; References; Index.

Editorial Reviews

"Excellent...In summary I warmly recommend a most rewarding and challenging textbook." Contemporary Physics, Professor D.S.F. Crothers

"This is a fine work that fills a long-standing void in the study of introductory mathematical physics." The Leading Edge, John Stockwell

From the Publisher