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
7 - Group-Walk Random Graphs
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. 190 - 204Publisher: Cambridge University PressPrint publication year: 2017
References
[1] . Negatively curved manifolds, elliptic operators, and the Martin boundary. The Annals of Mathematics, 125(3):495, 1987.Google Scholar
[2] . Positive harmonic functions and hyperbolicity. In Potential Theory Surveys and Problems, vol. 1344 of Lecture Notes in Mathematics, pp. 1–23. 1988.Google Scholar
[3] and . Recurrence of distributional limits of finite planar graphs. Electronic Journal of Probability, 6, 2001.Google Scholar
[4] , , , and . An Lp theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions. Preprint 2014.
[5] , , , , and . Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing. Advances in Mathematics, 6(6):1801–51, 2008.Google Scholar
[7] . Boundary properties of functions with finite Dirichlet integrals. Ann. Inst. Fourier, 12:573–621, 1962.Google Scholar
[9] and . Random Walks and Electrical Networks. Carus Mathematical Monographs 22, Mathematical Association of America, 1984.
[11] . Poisson–Furstenberg boundaries, large-scale geometry and growth of groups. In Proceedings of the ICM, pp. 681–704, 2010.Google Scholar
[12] . A Poisson formula for semi-simple Lie groups. The Annals of Mathematics, 2(2):335–86, 1963.Google Scholar
[13] . The boundary of a square tiling of a graph coincides with the poisson boundary. To appear in Invent. Math., DOI 10.1007/s00222-015-0601-0.
[14] . Electrical networks from the mathematical viewpoint. Lecture notes. In preparation.
[15] and . In preparation.
[16] . Random graphs and complex networks. Lecture Notes, 2013.
[17] . The poisson formula for groups with hyperbolic properties. The Annals of Mathematics, 152(3): 659–92, 2000.Google Scholar
[18] and . Random walks on discrete groups: boundary and entropy. The Annals of Probability, 3(3):457–90, 1983.Google Scholar
[19] . Random graphs from groups, 2014. Undergraduate research project. University of Warwick.
[20] . Sur le rôle de la frontière de R.S. Martin dans la théorie du potentiel. Annales Inst. Fourier, 7:183–281, 1957.Google Scholar
[21] and . One-dimensional 1/|ji |s percolation models: the existence of a transition for s ≤ 2. Commun. Math. Phys., 104:547–71, 1986.Google Scholar
[22] . Random Geometric Graphs. Oxford University Press, 2003.
[23] . Vacant set of random interlacements and percolation. Annals of Mathematics, 3(3):2039–2087, 2010.Google Scholar
[24] . Interlacement percolation on transient weighted graphs. 14:1604–27, 2009.
[25] . Resistances and currents in infinite electrical networks. J. Combin. Theory (Series B), 49:87–102, 1990.Google Scholar
[26] . Denumerable Markov Chains. Generating Functions, Boundary Theory, Random Walks on Trees. EMS Textbooks in Mathematics. European Mathematical Society (EMS), Zürich, 2009.
- 2
- Cited by