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. Athreya, Siva R.; Swart, Jan M. Survival of contact processes on the hierarchical group. Probab. Theory Related Fields 147 (2010), no. 3-4, 529--563. MR2639714
  2. Ben Arous, G.; Hryniv, O.; Molchanov, S. Phase transition for the spherical hierarchical model. Markov Process. Related Fields 8 (2002), no. 4, 565--594. MR1957220 (2004a:82031)
  3. Billingsley, Patrick. Probability and measure. Third edition. Wiley Series in Probability and Mathematical Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1995. xiv+593 pp. ISBN: 0-471-00710-2 MR1324786 (95k:60001)
  4. Brydges, David C.; Imbrie, John Z. Green's function for a hierarchical self-avoiding walk in four dimensions. Comm. Math. Phys. 239 (2003), no. 3, 549--584. MR2000929 (2004g:82043)
  5. Collet, Pierre; Eckmann, Jean-Pierre. A renormalization group analysis of the hierarchical model in statistical mechanics. Lecture Notes in Physics, Vol. 74. Springer-Verlag, Berlin-New York, 1978. i+199 pp. ISBN: 3-540-08670-6 MR0503070 (58 #19923)
  6. Cox, J. T.; Dawson, D. A.; Greven, A. Mutually catalytic super branching random walks: large finite systems and renormalization analysis. Mem. Amer. Math. Soc. 171 (2004), no. 809, viii+97 pp. MR2074427 (2005k:60298)
  7. Dawson, D. A.; Gorostiza, L. G. Percolation in a hierarchical random graph. Commun. Stoch. Anal. 1 (2007), no. 1, 29--47. MR2404371 (2009b:60296)
  8. Dawson, D. A.; Gorostiza, L. G. Percolation in an ultrametric space, on ArXiv:PR 1006.4400.
  9. Dawson, D. A.; Gorostiza, L. G.; Wakolbinger, A. Occupation time fluctuations in branching systems. J. Theoret. Probab. 14 (2001), no. 3, 729--796. MR1860521 (2002h:60183)
  10. Dawson, D. A.; Gorostiza, L. G.; Wakolbinger, A. Degrees of transience and recurrence and hierarchical random walks. Potential Anal. 22 (2005), no. 4, 305--350. MR2135263 (2006c:60055)
  11. Dawson, D. A.; Gorostiza, L. G.; Wakolbinger, A. Hierarchical random walks. Asymptotic methods in stochastics, 173--193, Fields Inst. Commun., 44, Amer. Math. Soc., Providence, RI, 2004. MR2106854 (2006i:60055)
  12. Dawson, D. A.; Gorostiza, L. G.; Wakolbinger, A. Hierarchical equilibria of branching populations. Electron. J. Probab. 9 (2004), no. 12, 316--381 (electronic). MR2080603 (2005i:60164)
  13. Dawson, Donald A.; Greven, A.. Hierarchical models of interacting diffusions: multiple time scale phenomena, phase transition and pattern of cluster-formation. Probab. Theory Related Fields 96 (1993), no. 4, 435--473. MR1234619 (94k:60155)
  14. Dawson, Donald A.; Greven, A.. Hierarchically interacting Fleming-Viot processes with selection and mutation: multiple space time scale analysis and quasi-equilibria. Electron. J. Probab. 4 (1999), no. 4, 81 pp. (electronic). MR1670873 (2000e:60139)
  15. Dawson, Donald A.; Greven, A.; Z?hle, I. Continuum limits of multitype population models on the hierarchical group (in preparation).
  16. Dyson, Freeman J. Existence of a phase-transition in a one-dimensional Ising ferromagnet. Comm. Math. Phys. 12 (1969), no. 2, 91--107. MR0436850 (55 #9786)
  17. Evans, Steven N. Local properties of Lévy processes on a totally disconnected group. J. Theoret. Probab. 2 (1989), no. 2, 209--259. MR0987578 (90g:60069)
  18. Evans, Steven N.; Fleischmann, Klaus. Cluster formation in a stepping-stone model with continuous, hierarchically structured sites. Ann. Probab. 24 (1996), no. 4, 1926--1952. MR1415234 (98g:60179)
  19. Flatto, Leopold; Pitt, Joel. Recurrence criteria for random walks on countable Abelian groups. Illinois J. Math. 18 (1974), 1--19. MR0341616 (49 #6363)
  20. Fleischmann, Klaus; Greven, Andreas. Diffusive clustering in an infinite system of hierarchically interacting diffusions. Probab. Theory Related Fields 98 (1994), no. 4, 517--566. MR1271108 (95j:60163)
  21. Greven, A. Multi-scale analysis of population models. Mathematical statistical physics, 547--605, Elsevier B. V., Amsterdam, 2006. MR2581893 (2011h:60206)
  22. Hambly, Ben; Jones, Liza. Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric $alpha$-stable processes. Electron. J. Probab. 12 (2007), no. 30, 862--887. MR2318413 (2008g:60144)
  23. Hambly, B. M.; Jones, L. A. Erratum to "Number variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric $alpha$-stable processes'' [ MR2318413]. Electron. J. Probab. 14 (2009), No. 37, 1074--1079. MR2506125 (2010i:60150)
  24. Kleinberg, J., Small-world phenomena and the dynamics of information, in ``Advances in Neural Information Processing Systems (NIPS)" 14 (2001), 431-438.
  25. Kleinberg, Jon. Complex networks and decentralized search algorithms. International Congress of Mathematicians. Vol. III, 1019--1044, Eur. Math. Soc., Zürich, 2006. MR2275717 (2007j:68121)
  26. Klenke, Achim. Different clustering regimes in systems of hierarchically interacting diffusions. Ann. Probab. 24 (1996), no. 2, 660--697. MR1404524 (97h:60125)
  27. Koval, S.; Meester, R.; Trapman, P., Long range percolation on a hierarchical lattice, ArXiv: PR 1004-1251.
  28. Kuttruf, S.; M¸ller, P.; Lifshits tails in the hierarchical Anderson model, Ann. I. H. Poincar'e (to appear).
  29. Sawyer, Stanley; Felsenstein, Joseph. Isolation by distance in a hierarchically clustered population. J. Appl. Probab. 20 (1983), no. 1, 1--10. MR0688075 (84h:92022)
  30. Spitzer, Frank. Principles of random walks. Second edition. Graduate Texts in Mathematics, Vol. 34. Springer-Verlag, New York-Heidelberg, 1976. xiii+408 pp. MR0388547 (52 #9383)

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