Two-Dimensional Random Walk
eBook - PDF

Two-Dimensional Random Walk

From Path Counting to Random Interlacements

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Two-Dimensional Random Walk

From Path Counting to Random Interlacements

About this book

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.

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Yes, you can access Two-Dimensional Random Walk by Serguei Popov in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half title
  3. Series page
  4. Title page
  5. Copyright information
  6. Contents
  7. Preface
  8. Notation
  9. 1 Introduction
  10. 2 Recurrence of two-dimensional simple random walk
  11. 3 Some potential theory for simple random walks
  12. 4 SRW conditioned on not hitting the origin
  13. 5 Intermezzo: soft local times and Poisson processes of objects
  14. 6 Random interlacements
  15. Hints and solutions to selected exercises
  16. References
  17. Index