Random Walk

Informationen zum Autor Gregory F. Lawler is Professor of Mathematics and Statistics at the University of Chicago. He received the George Pólya Prize in 2006 for his work with Oded Schramm and Wendelin Werner. Klappentext An advanced treatment of random walks written for students and researchers in probability and related fields. Zusammenfassung A random walk is one of the most studied topics in probability theory and has many important applications outside of mathematics. Ideal for graduate students! this text develops the theory from basic definitions through to current research problems. It is also suitable for mathematicians working in related fields. Inhaltsverzeichnis Preface; 1. Introduction; 2. Local central limit theorem; 3. Approximation by Brownian motion; 4. Green's function; 5. One-dimensional walks; 6. Potential theory; 7. Dyadic coupling; 8. Additional topics on simple random walk; 9. Loop measures; 10. Intersection probabilities for random walks; 11. Loop-erased random walk; Appendix; Bibliography; Index of symbols; Index.

Texte du rabat

An advanced treatment of random walks written for students and researchers in probability and related fields.

Résumé
A random walk is one of the most studied topics in probability theory and has many important applications outside of mathematics. Ideal for graduate students, this text develops the theory from basic definitions through to current research problems. It is also suitable for mathematicians working in related fields.

Contenu

Preface; 1. Introduction; 2. Local central limit theorem; 3. Approximation by Brownian motion; 4. Green's function; 5. One-dimensional walks; 6. Potential theory; 7. Dyadic coupling; 8. Additional topics on simple random walk; 9. Loop measures; 10. Intersection probabilities for random walks; 11. Loop-erased random walk; Appendix; Bibliography; Index of symbols; Index.