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

Joseph Rudnick; George Gaspari

doi:10.1017/CBO9780511610912

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.

Review of the hardback:'I warmly recommend a most rewarding and challenging textbook.'

Source: Contemporary Physics

Review of the hardback:'… an excellent starting point for those wanting a relatively simple and straightforward introduction to these topics.'

Source: Journal of Statistical Physics

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

Source: International Statistical Institute

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Elements of the Random Walk

An introduction for Advanced Students and Researchers

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xiv

1 - Introduction to techniques
pp 1-24

2 - Generating functions I
pp 25-50

3 - Generating functions II: recurrence, sites visited, and the role of dimensionality
pp 51-68

4 - Boundary conditions, steady state, and the electrostatic analogy
pp 69-94

5 - Variations on the random walk
pp 95-126

6 - The shape of a random walk
pp 127-166

7 - Path integrals and self-avoidance
pp 167-192

8 - Properties of the random walk: introduction to scaling
pp 193-202

9 - Scaling of walks and critical phenomena
pp 203-232

10 - Walks and the O(n) model: mean field theory and spin waves
pp 233-254

11 - Scaling, fractals, and renormalization
pp 255-284

12 - More on the renormalization group
pp 285-322

References
pp 323-326

Index
pp 327-329

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Elements of the Random Walk

An introduction for Advanced Students and Researchers

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