Probability Theory and Related Fields

, Volume 77, Issue 3, pp 401–413

Occupation time large deviations of the voter model

  • Maury Bramson
  • J. Theodore Cox
  • David Griffeath

DOI: 10.1007/BF00319297

Cite this article as:
Bramson, M., Theodore Cox, J. & Griffeath, D. Probab. Th. Rel. Fields (1988) 77: 401. doi:10.1007/BF00319297


This paper is a sequel to [5] and [6]. We continue our study of occupation time large deviation probabilities for some simple infinite particle systems by analysing the so-called voter model ζt (see e.g., [11] or [8]). In keeping with our previous results, we show that the large deviations are “classical” in high dimensions (d≧5 for ζt) but “fat” in low dimensions (d≦4). Interaction distinguishes the voter model from the independent particle systems of [5] and [6], and consequently exact computations no longer seem feasible. Instead, we derive upper and lower bounds which capture the asymptotic decay rate of the large deviation tails.

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Maury Bramson
    • 1
  • J. Theodore Cox
    • 2
  • David Griffeath
    • 3
  1. 1.Department of MathematicsUniversity of MinnesotaMineapolisUSA
  2. 2.Department of MathematicsSyracuse UniversitySyracuseUSA
  3. 3.Department of MathematicsUniversity of WisconsinMadisonUSA