Monotone interaction of walk and graph: recurrence versus transience

Amir Dembo (Stanford University)
Ruojun Huang (Stanford University)
Vladas Sidoravicius (IMPA)

Abstract


We consider recurrence versus transience for models of random walks on growing in time, connected subsets $\mathbb{G}_t$ of some fixed locally finite, connected graph, in which monotone interaction enforces such growth as a result of visits by the walk (or probes it sent), to the neighborhood of the boundary of $\mathbb{G}_t$.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 1-12

Publication Date: November 6, 2014

DOI: 10.1214/ECP.v19-3607

References

  • Amir, Gideon; Benjamini, Itai; Gurel-Gurevich, Ori; Kozma, Gady. Random walk in changing environment. Unpublished manuscript (2008).
  • Angel, Omer; Crawford, Nicholas; Kozma, Gady. Localization for linearly edge reinforced random walks. Duke Math. J. 163 (2014), no. 5, 889--921. MR3189433
  • Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas. Walking within growing domains: recurrence versus transience. Arxiv:1312.4610 (2013). To appear, Elec. J. Probab.
  • Disertori, Margherita; Sabot, Christophe; Tarre, Pierre. Transience of edge-reinforced random walk. arXiv:1403.6079v2 (2014).
  • Durrett, Rick. Probability: theory and examples. Fourth edition. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010. x+428 pp. ISBN: 978-0-521-76539-8 MR2722836
  • den Hollander, Frank; Molchanov, Stanislav A.; Zeitouni, Ofer. Random media at Saint-Flour. Reprints of lectures from the Annual Saint-Flour Probability Summer School held in Saint-Flour. Probability at Saint-Flour. Springer, Heidelberg, 2012. vi+564 pp. ISBN: 978-3-642-32948-7 MR3059554
  • Kozma, Gady. Reinforced random walk. Proc. of Europ. Cong. Math. (2012), 429-443.
  • Kozma, Gady. Centrally excited random walk is reccurent. Unpublished manuscript (2006).
  • Lawler, Gregory F. Intersections of random walks. Probability and its Applications. Birkhauser Boston, Inc., Boston, MA, 1991. 219 pp. ISBN: 0-8176-3557-2 MR1117680
  • Lawler, Gregory F.; Limic, Vlada. Random walk: a modern introduction. Cambridge Studies in Advanced Mathematics, 123. Cambridge University Press, Cambridge, 2010. xii+364 pp. ISBN: 978-0-521-51918-2 MR2677157
  • Sabot, Christophe; Tarres, Pierre. Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model. arXiv:1111.3991v4 (2012). To appear, J. Eur. Math. Soc.
Bookmark and Share


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