内容

目次

Part I. The Type Problem: 1. Basic facts; 2. Recurrence and transienceof infinite networks; 3. Applications to random walks; 4. Isoperimetricinequalities; 5. Transient subtrees, and the classification of the recurrentquasi transitive graphs; 6. More on recurrence; Part II. The Spectral Radius:7. Superharmonic functions and r-recurrence; 8. The spectral radius; 9.Computing the Green function; 10. Spectral radius and strong isoperimetricinequality; 11. A lower bound for simple random walk; 12. Spectral radius andamenability; Part III. The Asymptotic Behaviour of Transition Probabilities:13. The local central limit theorem on the grid; 14. Growth, isoperimetricinequalities, and the asymptotic type of random walk; 15. The asymptotic typeof random walk on amenable groups; 16. Simple random walk on the Sierpinskigraphs; 17. Local limit theorems on free products; 18. Intermezzo; 19. Freegroups and homogenous trees; Part IV. An Introduction to Topological BoundaryTheory: 20. Probabilistic approach to the Dirichlet problem, and a class ofcompactifications; 21. Ends of graphs and the Dirichlet problem; 22.Hyperbolic groups and graphs; 23. The Dirichlet problem for circle packinggraphs; 24. The construction of the Martin boundary; 25. Generalizedlattices, Abelian and nilpotent groups, and graphs with polynomial growth;27. The Martin boundary of hyperbolic graphs; 28. Cartesian products.