The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The development carefully provides the basic definitions of mutual intersection and self-intersection local times for Brownian motions and the accompanying large deviation results. The book then proceeds to the analogues of these concepts and results for random walks on lattices of \(R^d\). This includes suitable integrability and large deviation results for these models and some applications. Moreover, the notes and comments at the end of the chapters provide interesting remarks and references to various related results, as well as a good number of exercises. The author provides a beautiful development of these subtle topics at a level accessible to advanced graduate students.

Readership

Graduate students and research mathematicians interested in probability and statistical physics.

Reviews

"[T]he author is a leading expert who has made crucial contributions. ...This book covers a fascinating topic of current interest, collecting in one place and in a systematic way results that are scattered in the literature. Chen attempts to make the text essentially self-contained, and develops along the way the necessary tools. The book can be rather demanding in places but the motivated reader will draw many benefits from following the development."

-- Ofer Zeitouni, Mathematical Reviews