The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  • Aldous, David. Asymptotic fringe distributions for general families of random trees. Ann. Appl. Probab. 1 (1991), no. 2, 228--266. MR1102319
  • Aldous, David. Tree-based models for random distribution of mass. J. Statist. Phys. 73 (1993), no. 3-4, 625--641. MR1251658
  • Aldous, David; Lyons, Russell. Processes on unimodular random networks. Electron. J. Probab. 12 (2007), no. 54, 1454--1508. MR2354165
  • Athreya, Krishna B.; Ney, Peter E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040
  • Barlow, Martin T.; Kumagai, Takashi. Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 (2006), no. 1-4, ISBN: 0-9746986-1-X 33--65 (electronic). MR2247823
  • I. Benjamini and N. Curien. Ergodic theory on stationary random graphs. arxiv:1011.2526, 2010.
  • Benjamini, I.; Lyons, R.; Peres, Y.; Schramm, O. Group-invariant percolation on graphs. Geom. Funct. Anal. 9 (1999), no. 1, 29--66. MR1675890
  • Benjamini, Itai; Peres, Yuval. Markov chains indexed by trees. Ann. Probab. 22 (1994), no. 1, 219--243. MR1258875
  • Benjamini, Itai; Schramm, Oded. Recurrence of distributional limits of finite planar graphs. Electron. J. Probab. 6 (2001), no. 23, 13 pp. (electronic). MR1873300
  • Biggins, J. D. Chernoff's theorem in the branching random walk. J. Appl. Probability 14 (1977), no. 3, 630--636. MR0464415
  • N. Curien, L. Ménard, and G. Miermont. A view from infinity of the uniform infinite planar quadrangulation (in preparation). 2010.
  • Dawson, D. A.; Iscoe, I.; Perkins, E. A. Super-Brownian motion: path properties and hitting probabilities. Probab. Theory Related Fields 83 (1989), no. 1-2, 135--205. MR1012498
  • B. Durhuus. Probabilistic aspects of infinite trees and surfaces. Acta Physica Polonica B, 34:4795--4811, 2003.
  • Grimmett, G. R. Random labelled trees and their branching networks. J. Austral. Math. Soc. Ser. A 30 (1980/81), no. 2, 229--237. MR0607933
  • Kesten, Harry. Subdiffusive behavior of random walk on a random cluster. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 4, 425--487. MR0871905
  • Kesten, Harry. Branching random walk with a critical branching part. J. Theoret. Probab. 8 (1995), no. 4, 921--962. MR1353560
  • Le Gall, Jean-François. Spatial branching processes, random snakes and partial differential equations. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1999. x+163 pp. ISBN: 3-7643-6126-3 MR1714707
  • Le Gall, Jean-François. Random real trees. Ann. Fac. Sci. Toulouse Math. (6) 15 (2006), no. 1, 35--62. MR2225746
  • Lyons, Russell; Pemantle, Robin; Peres, Yuval. Conceptual proofs of $L\log L$ criteria for mean behavior of branching processes. Ann. Probab. 23 (1995), no. 3, 1125--1138. MR1349164
  • Lyons, Russell; Pemantle, Robin; Peres, Yuval. Ergodic theory on Galton-Watson trees: speed of random walk and dimension of harmonic measure. Ergodic Theory Dynam. Systems 15 (1995), no. 3, 593--619. MR1336708
  • R. Lyons and Y. Peres. Probability on Trees and Networks. Current version available at http://mypage.iu.edu/~rdlyons/, In preparation.
  • Stoeckl, Andreas; Wakolbinger, Anton. On clan-recurrence and -transience in time stationary branching Brownian particle systems. Measure-valued processes, stochastic partial differential equations, and interacting systems (Montreal, PQ, 1992), 213--219, CRM Proc. Lecture Notes, 5, Amer. Math. Soc., Providence, RI, 1994. MR1278296


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.