Elements of the random walk : an introduction for advanced students and researchers / Joseph Rudnick, George Gaspari.

Format:

Book

Author/Creator:

Rudnick, Joseph Alan, 1944- author.

Gaspari, George David, author.

Language:

English

Subjects (All):

Random walks (Mathematics).

Physical Description:

1 online resource (xv, 329 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2004.

Language Note:

English

Summary:

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.

Contents:

Cover; Half-title; Title; Copyright; Dedication; Contents; 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 groupReferences; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 323-325) and index.

ISBN:

1-107-14767-0

1-282-39477-0

9786612394775

0-511-64435-3

0-511-64813-8

0-511-18750-5

0-511-56649-2

0-511-61091-2

0-511-18657-6

OCLC:

569384451