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

  • Benjamini, Itai; Müller, Sebastian. On the trace of branching random walks. Groups Geom. Dyn. 6 (2012), no. 2, 231--247. MR2914859
  • Benjamini, Itai; Peres, Yuval. Markov chains indexed by trees. Ann. Probab. 22 (1994), no. 1, 219--243. MR1258875
  • Daniela Bertacchi and Fabio Zucca. Recent results on branching random walks. In Statistical Mechanics and Random Walks: Principles, Processes and Applications, pages 289--340. Nova Science Publishers, 2012.
  • Candellero, Elisabetta; Gilch, Lorenz A.; Müller, Sebastian. Branching random walks on free products of groups. Proc. Lond. Math. Soc. (3) 104 (2012), no. 6, 1085--1120. MR2946082
  • Hueter, Irene; Lalley, Steven P. Anisotropic branching random walks on homogeneous trees. Probab. Theory Related Fields 116 (2000), no. 1, 57--88. MR1736590
  • Lalley, Steven P. Growth profile and invariant measures for the weakly supercritical contact process on a homogeneous tree. Ann. Probab. 27 (1999), no. 1, 206--225. MR1681122
  • Lalley, Steven P.; Sellke, Tom. Limit set of a weakly supercritical contact process on a homogeneous tree. Ann. Probab. 26 (1998), no. 2, 644--657. MR1626499
  • Liggett, Thomas M. Branching random walks and contact processes on homogeneous trees. Probab. Theory Related Fields 106 (1996), no. 4, 495--519. MR1421990
  • Liggett, Thomas M. Multiple transition points for the contact process on the binary tree. Ann. Probab. 24 (1996), no. 4, 1675--1710. MR1415225
  • Lyons, Russell. Phase transitions on nonamenable graphs. Probabilistic techniques in equilibrium and nonequilibrium statistical physics. J. Math. Phys. 41 (2000), no. 3, 1099--1126. MR1757952
  • 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
  • Madras, Neal; Schinazi, Rinaldo. Branching random walks on trees. Stochastic Process. Appl. 42 (1992), no. 2, 255--267. MR1176500
  • Müller, Sebastian. Recurrence for branching Markov chains. Electron. Commun. Probab. 13 (2008), 576--605. MR2461533
  • Pemantle, Robin. The contact process on trees. Ann. Probab. 20 (1992), no. 4, 2089--2116. MR1188054
  • Pemantle, Robin; Stacey, Alan M. The branching random walk and contact process on Galton-Watson and nonhomogeneous trees. Ann. Probab. 29 (2001), no. 4, 1563--1590. MR1880232
  • Stacey, A. M. The existence of an intermediate phase for the contact process on trees. Ann. Probab. 24 (1996), no. 4, 1711--1726. MR1415226
  • Woess, Wolfgang. Random walks on infinite graphs and groups. Cambridge Tracts in Mathematics, 138. Cambridge University Press, Cambridge, 2000. xii+334 pp. ISBN: 0-521-55292-3 MR1743100


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