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


  1. Aidékon, Elie. Transient random walks in random environment on a Galton-Watson tree. Probab. Theory Related Fields 142 (2008), no. 3-4, 525--559. MR2438700
  2. Bercu, Bernard; Touati, Abderrahmen. Exponential inequalities for self-normalized martingales with applications. Ann. Appl. Probab. 18 (2008), no. 5, 1848--1869. MR2462551
  3. Biggins, J. D. Martingale convergence in the branching random walk. J. Appl. Probability 14 (1977), no. 1, 25--37. MR0433619
  4. Biggins, J. D.; Kyprianou, A. E. Seneta-Heyde norming in the branching random walk. Ann. Probab. 25 (1997), no. 1, 337--360. MR1428512
  5. Billingsley, Patrick. Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999. x+277 pp. ISBN: 0-471-19745-9 MR1700749
  6. Chernov A.A. Replication of a multicomponent chain. Biophysics 12 (1967), no. 2, 336--341.
  7. Faraud, G.; Hu, Y. Shi, ZAn almost sure convergence for stochastichally biased random walk on a Galton-Watson tree (2010). Arxiv
  8. Hu, Yueyun; Shi, Zhan. A subdiffusive behaviour of recurrent random walk in random environment on a regular tree. Probab. Theory Related Fields 138 (2007), no. 3-4, 521--549. MR2299718
  9. Hu, Yueyun; Shi, Zhan. Slow movement of random walk in random environment on a regular tree. Ann. Probab. 35 (2007), no. 5, 1978--1997. MR2349581
  10. Hu, Yueyun; Shi, Zhan. Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees. Ann. Probab. 37 (2009), no. 2, 742--789. MR2510023
  11. Kemeny, John G.; Snell, J. Laurie; Knapp, Anthony W. Denumerable Markov chains. Second edition. With a chapter on Markov random fields, by David Griffeath. Graduate Texts in Mathematics, No. 40. Springer-Verlag, New York-Heidelberg-Berlin, 1976. xii+484 pp. MR0407981
  12. Kipnis, C.; Varadhan, S. R. S. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104 (1986), no. 1, 1--19. MR0834478
  13. Liu, Quansheng. On generalized multiplicative cascades. Stochastic Process. Appl. 86 (2000), no. 2, 263--286. MR1741808
  14. Liu, Quansheng. Asymptotic properties and absolute continuity of laws stable by random weighted mean. Stochastic Process. Appl. 95 (2001), no. 1, 83--107. MR1847093
  15. Lyons, Russell. The Ising model and percolation on trees and tree-like graphs. Comm. Math. Phys. 125 (1989), no. 2, 337--353. MR1016874
  16. Lyons, Russell; Pemantle, Robin. Random walk in a random environment and first-passage percolation on trees. Ann. Probab. 20 (1992), no. 1, 125--136. MR1143414
  17. Lyons, Russell. Probability on trees and networks. (2005) Book
  18. Mandelbrot, Benoit. Multiplications aléatoires itérées et distributions invariantes par moyenne pondérée aléatoire: quelques extensions. C. R. Acad. Sci. Paris Sér. A 278 (1974), 355--358. MR0431352
  19. Menshikov, Mikhail; Petritis, Dimitri. On random walks in random environment on trees and their relationship with multiplicative chaos. Mathematics and computer science, II (Versailles, 2002), 415--422, Trends Math., Birkhäuser, Basel, 2002. MR1940150
  20. Neveu, J. Arbres et processus de Galton-Watson. (French) [Galton-Watson trees and processes] Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 2, 199--207. MR0850756
  21. Peres, Yuval; Zeitouni, Ofer. A central limit theorem for biased random walks on Galton-Watson trees. Probab. Theory Related Fields 140 (2008), no. 3-4, 595--629. MR2365486
  22. Petrov, V. V. Sums of independent random variables. Translated from the Russian by A. A. Brown. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 82. Springer-Verlag, New York-Heidelberg, 1975. x+346 pp. MR0388499
  23. Petrov, Valentin V. Limit theorems of probability theory. Sequences of independent random variables. Oxford Studies in Probability, 4. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. xii+292 pp. ISBN: 0-19-853499-X MR1353441
  24. Zeitouni, Ofer. Random walks in random environment. Lectures on probability theory and statistics, 189--312, Lecture Notes in Math., 1837, Springer, Berlin, 2004. MR2071631

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