Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Notation
- Part I Tools and Theory
- Part II Results and Applications
- 5 Growth, Dimension, and Heat Kernel
- 6 Bounded Harmonic functions
- 7 Choquet–Deny Groups
- 8 The Milnor–Wolf Theorem
- 9 Gromov’s Theorem
- Appendices
- Appendix A Hilbert Space Background
- Appendix B Entropy
- Appendix C Coupling and Total Variation
- References
- Index
7 - Choquet–Deny Groups
from Part II - Results and Applications
Published online by Cambridge University Press: 16 May 2024
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Notation
- Part I Tools and Theory
- Part II Results and Applications
- 5 Growth, Dimension, and Heat Kernel
- 6 Bounded Harmonic functions
- 7 Choquet–Deny Groups
- 8 The Milnor–Wolf Theorem
- 9 Gromov’s Theorem
- Appendices
- Appendix A Hilbert Space Background
- Appendix B Entropy
- Appendix C Coupling and Total Variation
- References
- Index
Summary
The Choquet–Deny theorem states that any random walk on a nilpotent group is Liouville. This theorem is presented and proved. We then present a recent result from 2018 by Frisch, Hartman, Tamuz, and Vahidi-Ferdowski, that these are basically the only such examples.
- Type
- Chapter
- Information
- Harmonic Functions and Random Walks on Groups , pp. 246 - 272Publisher: Cambridge University PressPrint publication year: 2024