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

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März 2004



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.


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.


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.


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
EAN: 9780521828918
ISBN: 0521828910
Untertitel: Sprache: Englisch.
Erscheinungsdatum: März 2004
Seitenanzahl: 329 Seiten
Format: gebunden
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