Electronic Communications in Probability

Monotone interaction of walk and graph: recurrence versus transience

Amir Dembo, Ruojun Huang, and Vladas Sidoravicius

Full-text: Open access

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 $\mathbb{G}_t$.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 76, 12 pp.

Dates
Accepted: 6 November 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316778

Digital Object Identifier
doi:10.1214/ECP.v19-3607

Mathematical Reviews number (MathSciNet)
MR3283607

Zentralblatt MATH identifier
1307.60140

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50] 60G50: Sums of independent random variables; random walks

Keywords
Recurrence interacting particle system reinforced random walk random walk on growing domains

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

Citation

Dembo, Amir; Huang, Ruojun; Sidoravicius, Vladas. Monotone interaction of walk and graph: recurrence versus transience. Electron. Commun. Probab. 19 (2014), paper no. 76, 12 pp. doi:10.1214/ECP.v19-3607. https://projecteuclid.org/euclid.ecp/1465316778


Export citation

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 Unpublished manuscript (2008).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.
  • 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
  • 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
  • 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
  • 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
  • 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.