Screen LibraryTwo-dimensional random walk : from path counting to random interlacements /
"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 resea...
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| Main Authors: | |
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| Published: |
Cambridge University Press,
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| Publisher Address: | Cambridge, United Kingdom : |
| Publication Dates: | 2021. |
| Literature type: | Book |
| Language: | English |
| Series: |
Institute of Mathematical Statistics textbooks ;
13 |
| Subjects: | |
| Summary: |
"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. The book starts with three different proofs of the recurrence of the two-dimensional walk, via direct combinatorial arguments, electrical networks, and Lyapunov functions. Then, 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 the book suitable for courses and for independent study."-- |
| Carrier Form: | 13, 209 pages : illustrations ; 23 cm. |
| Bibliography: | Includes bibliographical references (pages 201-207) and index. |
| ISBN: |
9781108472456 1108472451 9781108459693 1108459692 |
| Index Number: | QA274 |
| CLC: | O211.63 |
| Call Number: | O211.63/P829 |
| Contents: | Introduction -- Recurrence of two-dimensional simple random walk -- Some potential theory for simple random walks -- SRW conditioned on not hitting the origin -- Intermezzo: soft local times and Poisson processes of objects -- Random interlacements. |