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**Principles of random walk.
2nd ed. 1976, 2nd print.**
*(English)*
Zbl 0979.60002

Graduate Texts in Mathematics. 34. New York, NY: Springer. xiii, 408 p. (2001).

This is the second printing of the second edition from 1976. The first edition from 1964 soon became indispensable for those working on the field of random walks, see Zbl 0119.34304 for a detailed review of this edition. The most valuable new feature of the second edition is a supplementary bibliography covering results obtained from 1964 to 1976, which have been carefully included into the text.

The publication of the second printing now encourages the reader to reconstruct the trains of thought of the founders of the theory of random walk. Spitzer often shares his thoughts and intuition with the reader and does not only rely on mathematical formalisms. For those knowing already a little bit about the theory this book is an invaluable source of ideas, impressive connections and results. For those only just starting to learn about the subject the presentation might seem to be not as streamlined and graphically attractive as that of other introductory texts, but after some reading even beginners will hold the book in high esteem for its accuracy and well-chosen examples.

The publication of the second printing now encourages the reader to reconstruct the trains of thought of the founders of the theory of random walk. Spitzer often shares his thoughts and intuition with the reader and does not only rely on mathematical formalisms. For those knowing already a little bit about the theory this book is an invaluable source of ideas, impressive connections and results. For those only just starting to learn about the subject the presentation might seem to be not as streamlined and graphically attractive as that of other introductory texts, but after some reading even beginners will hold the book in high esteem for its accuracy and well-chosen examples.

Reviewer: Markus Reiß (Berlin)