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
8 - The Milnor–Wolf Theorem
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
This chapter is devoted to proving the Milnor–Wolf theorem, which states that a finitely generated solvable group has polynomial growth if and only if it is actually virtually nilpotent.
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- Harmonic Functions and Random Walks on Groups , pp. 273 - 300Publisher: Cambridge University PressPrint publication year: 2024