Random Walks on Infinite Graphs and Groups

摘要: Part I. The Type Problem: 1. Basic facts 2. Recurrence and transience of infinite networks 3. Applications to random walks 4. Isoperimetric inequalities 5. Transient subtrees, the classification recurrent quasi transitive graphs 6. More on recurrence II. Spectral Radius: 7. Superharmonic functions r-recurrence 8. spectral radius 9. Computing Green function 10. strong isoperimetric inequality 11. A lower bound for simple walk 12. amenability III. Asymptotic Behaviour Transition Probabilities: 13. local central limit theorem grid 14. Growth, inequalities, asymptotic type 15. amenable groups 16. Simple Sierpinski 17. Local theorems free products 18. Intermezzo 19. Free homogenous trees IV. An Introduction Topological Boundary Theory: 20. Probabilistic approach Dirichlet problem, a class compactifications 21. Ends problem 22. Hyperbolic 23. circle packing 24. construction Martin boundary 25. Generalized lattices, Abelian nilpotent groups, with polynomial growth 27. hyperbolic 28. Cartesian products.