Elements of the Random Walk

An introduction for Advanced Students and Researchers

Joseph Rudnick, George Gaspari

330 pages, parution le 02/04/2004

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Résumé

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 modern 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 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.

Sommaire

Introduction to techniques;
Generating functions I;
Generating functions II: recurrence, sites visited and the role of dimensionality;
Boundary conditions, steady state and the electrostatic analogy;
Variations on the random walk;
The shape of a random walk;
Path integrals and self-avoidance;
Properties of the random walk: introduction to scaling;
Scaling of walks and critical phenomena;
Walks and the O(n) model: mean field theory and spin waves;
Scaling, fractals and renormalization;
More on the renormalization group

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Joseph Rudnick, George Gaspari
Parution	02/04/2004
Nb. de pages	330
Format	17,5 x 25,5
Couverture	Relié
Poids	865g
Intérieur	Noir et Blanc
EAN13	9780521828918
ISBN13	978-0-521-82891-8