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

A self-contained introduction to the applications of random walk techniques.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. 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.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. 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.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 renormalizatilã9