Henze Very First Steps in Random Walks

The Power of Combinatorial Methods and Generating Functions
Erscheinungsjahr 2025
ISBN: 978-3-658-46313-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 17, 307 Seiten, eBook

Reihe: Mathematics Study Resources

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Henze, Norbert

Inhaltsverzeichnis

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.

Über Autor(innen)

Prof. Dr. Norbert Henze is a Professor of Stochastics at the Karlsruhe Institute of Technology (KIT), Institute of Stochastics, Karlsruhe, Germany. His well-established textbook  (Stochastik für Einsteiger) was first published in 1997.