Random walk in random and non-random environments.
2nd ed.

*(English)*Zbl 1090.60001
Hackensack, NJ: World Scientific (ISBN 981-256-361-X/hbk; 978-981-270-336-1/ebook). xvi, 380 p. (2005).

The book is a new edition of the 1990 book by P. Révész (1990; Zbl 0733.60091). A great number of papers and books on this subject have appeared in the last 16 years, and this new edition includes a number of those new results. Differences with respect to the first edition are notable in Parts I and II (Chapters 1–16 and Chapters 17–27) which discuss simple random walks in one dimension and more than one dimension. The second edition contains answers to some unsolved problems contained in the first edition. For instance, the answer to the fifth problem at p. 130 in the first edition is contained in Theorem 13.4, p. 158 of the second one. Also as an example, the third problem at p. 130 in the first edition is still open but one gives the strongest available result in Theorem 13.5, p. 158 of the second one. The second edition includes also some new results on frequently visited sites (in fact Sections 11.6 and 11.7 of the first one become Chapter 13 of the second one), on heavy points (Chapter 22 of the second edition) and on long excursions (Chapter 25 of the second edition). The reader interested on the theory of random walks in non-random environments and also on the associated strong limit laws will find this book very interesting and also very useful. The third part (Chapters 28–33) which concerns the random walks in random environments is not very different with respect to the first edition, although some recent progress on the topic could be noted.

Reviewer: Mihai Gradinaru (Nancy)

##### MSC:

60-02 | Research exposition (monographs, survey articles) pertaining to probability theory |

60G50 | Sums of independent random variables; random walks |

60J55 | Local time and additive functionals |

60K37 | Processes in random environments |

60F15 | Strong limit theorems |

60F17 | Functional limit theorems; invariance principles |