Book contents
- Frontmatter
- Contents
- Preface
- Conference Photographs
- 1 Growth of Groups and Wreath Products
- 2 Random Walks on Some Countable Groups
- 3 The Cost of Distinguishing Graphs
- 4 A Construction of the Measurable Poisson Boundary: From Discrete to Continuous Groups
- 5 Structure Trees, Networks and Almost Invariant Sets
- 6 Amenability of Trees
- 7 Group-Walk Random Graphs
- 8 Ends of Branching Random Walks on Planar Hyperbolic Cayley Graphs
- 9 Amenability and Ergodic Properties of Topological Groups: From Bogolyubov Onwards
- 10 Schreier Graphs of Grigorchuk's Group and a Subshift Associated to a Nonprimitive Substitution
- 11 Thompson's Group F is Not Liouville
- 12 A Proof of the Subadditive Ergodic Theorem
- 13 Boundaries of Zn-Free Groups
- 14 Buildings, Groups of Lie Type and Random Walks
- 15 On Some Random Walks Driven by Spread-Out Measures
- 16 Topics on Mathematical Crystallography
- References
2 - Random Walks on Some Countable Groups
Published online by Cambridge University Press: 20 July 2017
Book contents
- Frontmatter
- Contents
- Preface
- Conference Photographs
- 1 Growth of Groups and Wreath Products
- 2 Random Walks on Some Countable Groups
- 3 The Cost of Distinguishing Graphs
- 4 A Construction of the Measurable Poisson Boundary: From Discrete to Continuous Groups
- 5 Structure Trees, Networks and Almost Invariant Sets
- 6 Amenability of Trees
- 7 Group-Walk Random Graphs
- 8 Ends of Branching Random Walks on Planar Hyperbolic Cayley Graphs
- 9 Amenability and Ergodic Properties of Topological Groups: From Bogolyubov Onwards
- 10 Schreier Graphs of Grigorchuk's Group and a Subshift Associated to a Nonprimitive Substitution
- 11 Thompson's Group F is Not Liouville
- 12 A Proof of the Subadditive Ergodic Theorem
- 13 Boundaries of Zn-Free Groups
- 14 Buildings, Groups of Lie Type and Random Walks
- 15 On Some Random Walks Driven by Spread-Out Measures
- 16 Topics on Mathematical Crystallography
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Groups, Graphs and Random Walks , pp. 77 - 103Publisher: Cambridge University PressPrint publication year: 2017
References
[1] . A lower estimate for central probabilities on polycyclic group. Canad. J. Math., 5(5):897–910, 1992.Google Scholar
[2] and . Random walks on groups and discrete subordination. Math. Nachr., 285(5-6):580–605, 2012.Google Scholar
[3] and . Long time behavior of random walks on abelian groups. Colloq. Math., 2(2):445–64, 2010.Google Scholar
[4] , , and . Spectral properties of a class of random walks on locally finite groups. Groups Geom. Dyn., 4(4):791–820, 2013.Google Scholar
[5] and . Random walks driven by low moment measures. Ann. Probab., 6(6):2539–88, 2012.Google Scholar
[6] , , and . Regular Variation, Volume 27 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1989.
[7] and . On transience of card shuffling. Proc. Amer. Math. Soc., 5(5):1513–19, 2001.Google Scholar
[8] and . Comparison techniques for random walk on finite groups. Ann. Probab., 4(4):2131–56, 1993.Google Scholar
[9] and . Random walks on abelian groups with an infinite number of generators. Vestnik Moskov. Univ. Ser. I Mat. Mekh., (5):22–9, 1978.Google Scholar
[10] . Generating random elements in SLn(Fq) by random transvections. J. Algebraic Combin., 2(2):133–50, 1992.Google Scholar
[12] , , and . Finite simple groups as expanders. Proc. Natl. Acad. Sci. USA, 103(16): 6116–119 (electronic), 2006.Google Scholar
[13] and . Random walk on countably infinite Abelian groups. Acta Math., 114:237–65, 1965.Google Scholar
[14] . Recurrence and transience for a card shuffling model. Combin. Probab. Comput., 2(2):133–42, 1995.Google Scholar
[16] and . On the stability of the behavior of random walks on groups. J. Geom. Anal., 4(4):713–37, 2000.Google Scholar
[17] . Probability on groups: random walks and invariant diffusions. Notices Amer. Math. Soc., 9(9):968–77, 2001.Google Scholar
[18] . Analysis on Riemannian co-compact covers. In Surveys in differential geometry. Vol. IX, Surv. Differ. Geom., IX, pp. 351–84. Int. Press, Somerville, MA, 2004.
[19] . Random walks on finite groups. In Probability on Discrete Structures, Volume 110 of Encyclopaedia Math. Sci., pp. 263–346. Springer, Berlin, 2004.
[20] . Eigenvalues of the natural random walk on the Burnside group B(3, n). Ann. Probab., 4(4):1950–60, 1995.Google Scholar
[21] , , and . Analysis and Geometry on Groups, Volume 100 of Cambridge Tracts in Mathematics. Cambridge University Press, 1992.
[22] . Random Walks on Infinite Graphs and Groups, Volume 138 of Cambridge Tracts in Mathematics. Cambridge University Press, 2000.
- 1
- Cited by