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

Autor Joseph Rudnick, George Gaspari
en Limba Engleză Paperback – 24 mar 2010
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.
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Specificații

ISBN-13: 9780521535830
ISBN-10: 0521535832
Pagini: 348
Ilustrații: 104 b/w illus. 2 tables 97 exercises
Dimensiuni: 170 x 244 x 18 mm
Greutate: 0.55 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

Review of the hardback: 'I warmly recommend a most rewarding and challenging textbook.' Contemporary Physics
Review of the hardback: '… an excellent starting point for those wanting a relatively simple and straightforward introduction to these topics.' Journal of Statistical Physics
Review of the hardback: '… an excellent introduction to emerging topics such as fractals, scaling and path integrals.' International Statistical Institute

Descriere

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