Electronic Communications in Probability

Disjoint crossings, positive speed and deviation estimates for first passage percolation

Ghurumuruhan Ganesan

Full-text: Open access

Abstract

Consider bond percolation on the square lattice \(\mathbb{Z}^2\) where each edge is independently open with probability \(p.\) For some positive constants \(p_0 \in

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 52, 8 pp.

Dates
Accepted: 11 August 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316754

Digital Object Identifier
doi:10.1214/ECP.v19-3490

Mathematical Reviews number (MathSciNet)
MR3246971

Zentralblatt MATH identifier
1320.60156

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

Citation

Ganesan, Ghurumuruhan. Disjoint crossings, positive speed and deviation estimates for first passage percolation. Electron. Commun. Probab. 19 (2014), paper no. 52, 8 pp. doi:10.1214/ECP.v19-3490. https://projecteuclid.org/euclid.ecp/1465316754


Export citation

References

  • Bollobas, Bela; Riordan, Oliver. Percolation. Cambridge University Press, New York, 2006. x+323 pp. ISBN: 978-0-521-87232-4; 0-521-87232-4
  • Durrett, Richard. Oriented percolation in two dimensions. Ann. Probab. 12 (1984), no. 4, 999–1040.
  • Durrett, Richard. Probability: theory and examples. Second edition. Duxbury Press, Belmont, CA, 1996. xiii+503 pp. ISBN: 0-534-24318-5
  • Kesten, Harry. On the speed of convergence in first-passage percolation. Ann. Appl. Probab. 3 (1993), no. 2, 296–338.
  • Smythe, R. T.; Wierman, John C. First-passage percolation on the square lattice. Lecture Notes in Mathematics, 671. Springer, Berlin, 1978. viii+196 pp. ISBN: 3-540-08928-4