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

  1. Athreya, K.B.; Ney, P. E. Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040 (51 #9242)
  2. Benjamini, I.; Peres, Y. Markov chains indexed by trees. Ann. Probab. 22 (1994), no. 1, 219--243. MR1258875 (94j:60131)
  3. Benjamini, I.; Peres, Y. Tree-indexed random walks on groups and first passage percolation. Probab. Theory Related Fields 98 (1994), no. 1, 91--112. MR1254826 (94m:60141)
  4. Biggins, J. D. The first- and last-birth problems for a multitype age-dependent branching process. Advances in Appl. Probability 8 (1976), no. 3, 446--459. MR0420890 (54 #8901)
  5. Comets, F.; Menshikov, M. V.; Popov, S. Yu. One-dimensional branching random walk in a random environment: a classification. I Brazilian School in Probability (Rio de Janeiro, 1997). Markov Process. Related Fields 4 (1998), no. 4, 465--477. MR1677053 (2000c:60131)
  6. Comets, Francis; Popov, Serguei. On multidimensional branching random walks in random environment. Ann. Probab. 35 (2007), no. 1, 68--114. MR2303944 (2007k:60336)
  7. Dembo, A.; Zeitouni, O. Large deviations techniques and applications. Second edition. Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030)
  8. den Hollander, F.; Menshikov, M. V.; Popov, S. Yu. A note on transience versus recurrence for a branching random walk in random environment. J. Statist. Phys. 95 (1999), no. 3-4, 587--614. MR1700867 (2000k:60206)
  9. Fayolle, G.; Malyshev, V. A.; Menshikov, M. V. Topics in the constructive theory of countable Markov chains. Cambridge University Press, Cambridge, 1995. iv+169 pp. ISBN: 0-521-46197-9 MR1331145 (96k:60174)
  10. Gantert, N.; M¸ller, S. The critical branching Markov chain is transient. Markov Process. Related Fields. 12 (2006), no. 4, 805--814. MR2284404 (2008c:60082)
  11. Hammersley, J. M. Postulates for subadditive processes. Ann. Probability 2 (1974), 652--680. MR0370721 (51 #6947)
  12. Hueter, I.; Lalley, Steven P. Anisotropic branching random walks on homogeneous trees. Probab. Theory Related Fields 116 (2000), no. 1, 57--88. MR1736590 (2001f:60094)
  13. Kingman, J. F. C. The first birth problem for an age-dependent branching process. Ann. Probability 3 (1975), no. 5, 790--801. MR0400438 (53 #4271)
  14. Lyons, R. Random walks and percolation on trees. Ann. Probab. 18 (1990), no. 3, 931--958. MR1062053 (91i:60179)
  15. R. Lyons, with Y. Peres. Probability on Trees and Networks. Cambridge University Press. In preparation. Current version available at http://mypage.iu.edu/~rdlyons
  16. Machado, F. P.; Popov, S. Yu. One-dimensional branching random walks in a Markovian random environment. J. Appl. Probab. 37 (2000), no. 4, 1157--1163. MR1808881 (2002f:60141)
  17. Machado, F. P.; Popov, S. Yu. Branching random walk in random environment on trees. Stochastic Process. Appl. 106 (2003), no. 1, 95--106. MR1983045 (2005e:60238)
  18. Menshikov, M. V.; Volkov, S. E. Branching Markov chains: qualitative characteristics. Markov Process. Related Fields 3 (1997), no. 2, 225--241. MR1468175 (99c:60192)
  19. Menshikov, M.; Petritis, D.; Volkov, S. Random environment on coloured trees. Bernoulli 13 (2007), no. 4, 966--980. MR2364222 (2008k:60255)
  20. M¸ller, S. Recurrence and transience for branching random walks in an iid random environment. Markov Process. Related Fields. 14 (2008), no. 1, 115--130. MR2433298
  21. M¸ller, S. A criterion for transience of multidimensional branching random walk in random environment. Electr. J. of Probab. 13 (2008), 1189--1202. Math. Review number not available.
  22. Nagnibeda, T.; Woess, W. Random walks on trees with finitely many cone types. J. Theoret. Probab. 15 (2002), no. 2, 383--422. MR1898814 (2003k:60098)
  23. Pemantle, R.; Stacey, A. M. The branching random walk and contact process on Galton-Watson and nonhomogeneous trees. Ann. Probab. 29 (2001), no. 4, 1563--1590. MR1880232 (2002m:60193)
  24. Peres, Y. Probability on trees: an introductory climb. Lectures on probability theory and statistics (Saint-Flour, 1997), 193--280, Lecture Notes in Math., 1717, Springer, Berlin, 1999. MR1746302 (2001c:60139)
  25. Schinazi, R. On multiple phase transitions for branching Markov chains. J. Statist. Phys. 71 (1993), no. 3-4, 507--511. MR1219019 (94c:60141)
  26. Stacey, A. Branching random walks on quasi-transitive graphs. Combinatorics, probability and computing (Oberwolfach, 2001). Combin. Probab. Comput. 12 (2003), no. 3, 345--358. MR1988981 (2004d:60223)
  27. Vere-Jones, D. Ergodic properties of nonnegative matrices. I. Pacific J. Math. 22 1967 361--386. MR0214145 (35 #4996)
  28. Volkov, S. Branching random walk in random environment: fully quenched case. Markov Process. Related Fields 7 (2001), no. 2, 349--353. MR1856501 (2003e:60195)
  29. Woess, W. 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 (2001k:60006)
  30. Woess, W. Denumerable Markov Chains. To appear.


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