Random Walks on Infinite Graphs and Groups

€ 71,99
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Januar 2008



The main theme of this book is the interplay between random walks and discrete structure theory.


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, and the classification of the recurrent quasi 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 isoperimetric inequality; 11. A lower bound for simple random walk; 12. Spectral radius and amenability; Part III. The Asymptotic Behaviour of Transition Probabilities: 13. The local central limit theorem on the grid; 14. Growth, isoperimetric inequalities, and the asymptotic type of random walk; 15. The asymptotic type of random walk on amenable groups; 16. Simple random walk on the Sierpinski graphs; 17. Local limit theorems on free products; 18. Intermezzo; 19. Free groups and homogenous trees; Part IV. An Introduction to Topological Boundary Theory: 20. Probabilistic approach to the Dirichlet problem, and a class of compactifications; 21. Ends of graphs and the Dirichlet problem; 22. Hyperbolic groups and graphs; 23. The Dirichlet problem for circle packing graphs; 24. The construction of the Martin boundary; 25. Generalized lattices, Abelian and nilpotent groups, and graphs with polynomial growth; 27. The Martin boundary of hyperbolic graphs; 28. Cartesian products.


Review of the hardback: 'This is an excellent book, where beginners and specialists alike will find useful information. It will become one of the major references for all those interested directly or indirectly in random walks. I highly recommend it.' L. Saloff-Coste, Bulletin of the London Mathematical Society Review of the hardback: '... will be essential reading for all researchers in stochastic processes and related topics.' European Maths Society Journal
EAN: 9780521061728
ISBN: 0521061725
Untertitel: 'Cambridge Tracts in Mathematic'. Sprache: Englisch.
Erscheinungsdatum: Januar 2008
Seitenanzahl: 352 Seiten
Format: kartoniert
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