Very First Steps in Random Walks
The Power of Combinatorial Methods and Generating Functions
Series: Mathematics Study Resources; 17;
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Product details:
- Edition number 2025
- Publisher Springer Spektrum Wiesbaden
- Date of Publication 12 February 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783658463120
- Binding Paperback
- No. of pages307 pages
- Size 235x155 mm
- Language English
- Illustrations VIII, 307 p. 110 illus., 89 illus. in color. Illustrations, black & white 713
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Long description:
With this book, which is based on the third edition of a book first written in German about random walks, the author succeeds in a remarkably playful manner in captivating the reader with numerous surprising random phenomena and non-standard limit theorems related to simple random walks and related topics. The work stands out with its consistently problem-oriented, lively presentation, which is further enhanced by 100 illustrative images. The text includes 53 self-assessment questions, with answers provided at the end of each chapter.
Additionally, 74 exercises with solutions assist in understanding the material deeply. The text frequently engages in concrete model-building, and the resulting findings are thoroughly discussed and interconnected. Students who have tested this work in introductory seminars on stochastics were particularly fascinated by the interplay of geometric arguments (reflection principle), combinatorics, elementary stochastics, and analysis.
This book is a translation of an original German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.
MoreTable of Contents:
1 Introduction.- 2 The Simple Symmetric Random Walk on Z.- 3 Bridges: The Tied-down Random Walk.- 4 Asymmetric Random Walks on Z and Related Topics.- 5 Random Walks on the Integer Lattice Zd.- 6 Outlook.- 7 Tools from Stochastics, Combinatorics, and Analysis.- Solutions to the Exercises.- Bibliography.
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