Random walks, spectral radii, and Ramanujan graphs

Chapters in this book

1. Frontmatter I
2. Table of contents IX
3. Surveys and longer articles
4. Some Markov chains on abelian groups with applications 3
5. Random walks and physical models on infinite graphs: an introduction 35
6. The Garden of Eden Theorem for cellular automata and for symbolic dynamical systems 73
7. Expander graphs, random matrices and quantum chaos 109
8. The Ihara zeta function of infinite graphs, the KNS spectral measure and integrable maps 141
9. Simplicité de spectres de Lyapounov et propriété d’isolation spectrale pour une famille d’opérateurs de transfert sur l’espace projectif 181
10. An introduction to the Stochastic Loewner Evolution 261
11. A canonical form for automorphisms of totally disconnected locally compact groups 295
12. Research communications
13. On the classification of invariant measures for horosphere foliations on nilpotent covers of negatively curved manifolds 319
14. Markov processes on vermiculated spaces 337
15. Cactus trees and lower bounds on the spectral radius of vertex-transitive graphs 349
16. Equilibrium measure, Poisson kernel and effective resistance on networks 363
17. Internal diffusion limited aggregation on discrete groups of polynomial growth 377
18. On the physical relevance of random walks: an example of random walks on a randomly oriented lattice 393
19. Random walks, entropy and hopfianity of free groups 413
20. Growth rates of small cancellation groups 421
21. Recurrence properties of random walks on finite volume homogeneous manifolds 431
22. On the cohomology of foliations with amenable groupoid 445
23. Linear rate of escape and convergence in direction 459
24. Remarks on harmonic functions on affine buildings 473
25. Random walks, spectral radii, and Ramanujan graphs 487
26. Cogrowth of arbitrary graphs 501
27. Total variation lower bounds for finite Markov chains: Wilson’s lemma 515
28. Backmatter 531