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

A self-contained introduction to the applications of random walk techniques.

Joseph Rudnick (Author), George Gaspari (Author)

9780521828918, Cambridge University Press

Hardback, published 4 March 2004

346 pages
24.4 x 17 x 2.1 cm, 0.75 kg

Review of the hardback: '… an excellent introduction to emerging topics such as fractals, scaling and path integrals.' International Statistical Institute

Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This 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.

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.

Subject Areas: Earth sciences [RB], Molecular biology [PSD], Physical chemistry [PNR], Condensed matter physics [liquid state & solid state physics PHFC], Physics [PH], Applied mathematics [PBW]