Random Walk: A Modern Introduction
Cambridge Studies in Advanced Mathematics Series

Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

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.

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.
Vlada Limic works as a researcher for Centre National de la Recherche Scientifique (CNRS) at Université de Provence, Marseilles.