Elements of the Random Walk

Erscheinungsjahr 2015
ISBN: 978-0-521-82891-8
Verlag: Cambridge University Press

Buch, Englisch, 346 Seiten, Format (B × H): 175 mm x 250 mm, Gewicht: 777 g

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.

Autoren/Hrsg.

Rudnick, Joseph

Gaspari, George

Fachgebiete

• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Vorklinische Medizin: Grundlagenfächer Humangenetik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Naturwissenschaften Biowissenschaften Molekularbiologie
• Naturwissenschaften Biowissenschaften Proteinforschung
• Naturwissenschaften Chemie Physikalische Chemie
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Naturwissenschaften Physik Physik Allgemein

Inhaltsverzeichnis

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.

Über Autor(innen)

Rudnick, Joseph
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.

Gaspari, George
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.