ENGLISH

Two-Dimensional Random Walk

By Serguei Popov

Book information

Publisher
Cambridge University Press
Year
2021
ISBN
9781108472456, 9781108680134, 2020020947, 2020020948, 9781108459693
Language
english
Format
PDF
Filesize
2 MB (2311793 bytes)
Series
IMS Textbooks
Edition
1
Pages
207\224
Time added
2020-12-16 14:55:25
Markov ChainMartingalePotential TheoryRandom InterlacementsRecurrence

Description

The main subject of this introductory book is simple random walk on the integerlattice, with special attention to the two-dimensional case. This fascinatingmathematical object is the point of departure for an intuitive and richly illustrated tourof related topics at the active edge of research. The book starts with three differentproofs of the recurrence of the two-dimensional walk, via direct combinatorialarguments, electrical networks, and Lyapunov functions. Then, after reviewing somerelevant potential-theoretic tools, the reader is guided towards the relatively new topicof random interlacements – which can be viewed as a “canonical soup” ofnearest-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 areconstructed and review the recently introduced method of soft local times. Eachchapter ends with many exercises, making the book suitable for courses and forindependent study.

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