Electronic Communications in Probability

From survival to extinction of the contact process by the removal of a single edge

Réka Szabó and Daniel Valesin

Full-text: Open access

Abstract

We give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge $e^*$ is removed, one obtains two subtrees in which the contact process with infection rate smaller than $1/4$ dies out.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 54, 8 pp.

Dates
Received: 25 January 2016
Accepted: 19 July 2016
First available in Project Euclid: 25 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1472144932

Digital Object Identifier
doi:10.1214/16-ECP11

Mathematical Reviews number (MathSciNet)
MR3548766

Zentralblatt MATH identifier
1348.82058

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35]

Keywords
interacting particle systems contact process phase transition

Rights
Creative Commons Attribution 4.0 International License.

Citation

Szabó, Réka; Valesin, Daniel. From survival to extinction of the contact process by the removal of a single edge. Electron. Commun. Probab. 21 (2016), paper no. 54, 8 pp. doi:10.1214/16-ECP11. https://projecteuclid.org/euclid.ecp/1472144932


Export citation

References

  • [1] Berger, N., Borgs, C., Chayes, J. T. and Saberi, A.: On the spread of viruses on the internet. ACM-SIAM Symposium on Discrete Algorithms, New York (2005), 301–310.
  • [2] Handjani, S. J.: Inhomogeneous voter models in one dimension. J. Theoret. Probab. 16, (2003), no. 2, 325–338.
  • [3] Jung, P.: The critical value of the contact process with added and removed edges. J. Theoret. Probab. 18, (2005), no. 4, 949–955.
  • [4] Liggett, T.: Interacting Particle Systems. Springer, New York (1985),
  • [5] Liggett, T.: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, New York (1999),
  • [6] Madras, N., Schinazi, R. and Schonmann, R. H.: On the critical behavior of the contact process in deterministic inhomogeneous environments. Ann. Probab. 22, (1994), no. 3, 1140–1159.,
  • [7] Mountford, T., Valesin, D. and Yao, Q.: Metastable densities for the contact process on power law random graphs. Electron. J. Probab. 18, (2013), no. 103, 1–36.
  • [8] Newman, C. and Volchan, S.: Persistent survival of one-dimensional contact processes in random environments. Ann. Probab. 24, (1996), no. 1, 411–421.
  • [9] Pemantle, R. and Stacey, A. M.: The branching random walk and contact process on nonhomogeneous and Galton–Watson trees. Ann. Probab. 29, (2001), no. 4, 1563–1590.