Probability Theory and Related Fields

, Volume 106, Issue 4, pp 559–591

Superdiffusivity in first-passage percolation

  • C. Licea
  • C.M. Newman
  • M.S.T. Piza

DOI: 10.1007/s004400050075

Cite this article as:
Licea, C., Newman, C. & Piza, M. Probab Theory Relat Fields (1996) 106: 559. doi:10.1007/s004400050075

Summary.

In standard first-passage percolation on \({\Bbb Z}^d\) (with \(d\geq 2\)), the time-minimizing paths from a point to a plane at distance \(L\) are expected to have transverse fluctuations of order \(L^\xi\). It has been conjectured that \(\xi(d)\geq 1/2\) with the inequality strict (superdiffusivity) at least for low \(d\) and with \(\xi(2)=2/3\). We prove (versions of) \(\xi(d)\geq 1/2\) for all \(d\) and \(\xi(2)\geq 3/5\).

Mathematics Subject Classification (1991):60K35, 82C24, 82B24, 82B44

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • C. Licea
    • 1
  • C.M. Newman
    • 2
  • M.S.T. Piza
    • 3
  1. 1.Courant Institute of Mathematical Sciences, New York UniversityUS
  2. 2.Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012, USA (e-mail: newman@cims.nyu.edu)US
  3. 3.Department of Mathematics, University of California, Irvine, CA 92717, USAUS