Two-Dimensional Random Walk (Hardcover) (ISBN-13: 9781108472456)

The main subject of this introductory book is simple random walk on the integer lattice, with special attention to the two-dimensional case. This fascinating mathematical object is the point of departure for an intuitive and richly illustrated tour of related topics at the active edge of research. It starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. After reviewing some relevant potential-theoretic tools, the reader is guided toward the relatively new topic of random interlacements - which can be viewed as a 'canonical soup' of nearest-neighbour loops through infinity - again with emphasis on two dimensions. On the way, readers will visit conditioned simple random walks - which are the 'noodles' in the soup - and also discover how Poisson processes of infinite objects are constructed and review the recently introduced method of soft local times. Each chapter ends with many exercises, making it suitable for courses and independent study.

Author: Serguei Popov
ISBN-10: 1108472451
ISBN-13: 9781108472456
Publisher: Cambridge University Press
Language: English
Published: 03/18/2021
Pages: 200
Format: Hardcover
Weight: 1.03lbs
Size: 9.00h x 6.00w x 0.56d

Review Citation(s):
Choice 08/01/2022