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

  • Benaïm, Michel. Vertex-reinforced random walks and a conjecture of Pemantle. Ann. Probab. 25 (1997), no. 1, 361--392. MR1428513
  • Benaïm, M. and Tarrès, P.: Dynamics of Vertex-Reinforced Random Walks, to appear in phAnn. Probab.
  • Cranston, M.; Le Jan, Y. Self-attracting diffusions: two case studies. Math. Ann. 303 (1995), no. 1, 87--93. MR1348356
  • Erschler A., Tóth B., Werner W.: Some locally self-interacting walks on the integers, ARXIV1011.1102.
  • Erschler A., Tóth B., Werner W.: Stuck Walks, to appear in phProbab. Theory Related Fields.
  • Herrmann, Samuel; Roynette, Bernard. Boundedness and convergence of some self-attracting diffusions. Math. Ann. 325 (2003), no. 1, 81--96. MR1957265
  • Limic, Vlada; Volkov, Stanislav. VRRW on complete-like graphs: almost sure behavior. Ann. Appl. Probab. 20 (2010), no. 6, 2346--2388. MR2759737
  • Pemantle, Robin. Vertex-reinforced random walk. Probab. Theory Related Fields 92 (1992), no. 1, 117--136. MR1156453
  • Pemantle, Robin; Volkov, Stanislav. Vertex-reinforced random walk on ${\bf Z}$ has finite range. Ann. Probab. 27 (1999), no. 3, 1368--1388. MR1733153
  • Raimond, Olivier. Self-attracting diffusions: case of the constant interaction. Probab. Theory Related Fields 107 (1997), no. 2, 177--196. MR1431218
  • Tarrès, Pierre. Vertex-reinforced random walk on $\Bbb Z$ eventually gets stuck on five points. Ann. Probab. 32 (2004), no. 3B, 2650--2701. MR2078554
  • Tarrès P.: Localization of reinforced random walks, ARXIV1103.5536.
  • Volkov, Stanislav. Vertex-reinforced random walk on arbitrary graphs. Ann. Probab. 29 (2001), no. 1, 66--91. MR1825142
  • Volkov, Stanislav. Phase transition in vertex-reinforced random walks on $\Bbb Z$ with non-linear reinforcement. J. Theoret. Probab. 19 (2006), no. 3, 691--700. MR2280515


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