Random Walks and Random Environments: Volume 1: Random Walks

Volume 1 can be read without reference to Volume 2. In Volume 1, I expect of the reader only a modest facility in classical analysis, including the theory of functions of a complex variable up to contour integration. Those elements of probability theory which are needed are introduced in Chapter 1 of Volume 1, so that although an acquaintance with elementary probability theory is helpful, it is not essential. Appendices to Volume 1 supply useful results involving special functions and some mathematical techniques which are useful in the study of random walks. Drawing only on Volume 1, a short course on the classical theory of random walks and their applications may be based on the core material of Chapter 1, §2.1- §2.2 of Chapter 2, and Chapters 3, 4, and 6, with a more substantial course drawing on some of Chapter 5, and additional material from Chapter 2. Chapters 1 and 7 are the basis of a course on the self-avoiding walk.