Two-Dimensional Random Walk - Serguei Popov

Two-Dimensional Random Walk

From Path Counting to Random Interlacements

(Autor)

Buch | Hardcover
200 Seiten
2021
Cambridge University Press (Verlag)
978-1-108-47245-6 (ISBN)
137,15 inkl. MwSt
This book revolves around two-dimensional simple random walk, a rich and fascinating mathematical object that is the point of departure for a tour of related topics at the active edge of research. Emphasizing direct probabilistic intuition - with many illustrations - it is a highly readable introduction for graduate students and researchers.
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.

1. Introduction; 2. Recurrence of Two-Dimensional SRW; 3. Some Potential Theory for Simple Random Walks; 4. SRW Conditioned on not Hitting the Origin; 5. Intermezzo: Soft Local Times and Poisson Processes of Objects; 6. Random Interlacements.

Erscheinungsdatum
Reihe/Serie Institute of Mathematical Statistics Textbooks
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 160 x 235 mm
Gewicht 470 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
ISBN-10 1-108-47245-1 / 1108472451
ISBN-13 978-1-108-47245-6 / 9781108472456
Zustand Neuware
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