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


  • Alves, O. S. M.; Machado, F. P.; Popov, S. Yu. The shape theorem for the frog model. Ann. Appl. Probab. 12 (2002), no. 2, 533--546. MR1910638
  • Alves, O. S. M.; Machado, F. P.; Popov, S. Yu.; Ravishankar, K. The shape theorem for the frog model with random initial configuration. Markov Process. Related Fields 7 (2001), no. 4, 525--539. MR1893139
  • 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
  • Hughes, Barry D. Random walks and random environments. Vol. 1. Random walks. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1995. xxii+631 pp. ISBN: 0-19-853788-3 MR1341369
  • Lawler, Gregory F. Intersections of random walks. Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1991. 219 pp. ISBN: 0-8176-3557-2 MR1117680
  • sc M.V. Menshikov (1985) Estimates for percolation thresholds for lattices in bbR^n. Soviet Math. Dokl. 32 (2), 368--370.
  • Menʹshikov, M. V. Quantitative estimates and strong inequalities for the critical points of a graph and its subgraph. (Russian) Teor. Veroyatnost. i Primenen. 32 (1987), no. 3, 599--602. MR0914957
  • Popov, S. Yu. Frogs in random environment. J. Statist. Phys. 102 (2001), no. 1-2, 191--201. MR1819703
  • sc A. Shiryaev (1989) Probability (2nd. ed.). Springer, New York.
  • Telcs, András; Wormald, Nicholas C. Branching and tree indexed random walks on fractals. J. Appl. Probab. 36 (1999), no. 4, 999--1011. MR1742145

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