• Bernoulli
  • Volume 12, Number 1 (2006), 101-111.

The reversible nearest particle system on a finite interval

Dayue Chen, Juxin Liu, and Fuxi Zhang

Full-text: Open access


We study a one-parameter family of attractive reversible nearest particle systems on a finite interval. As the length of the interval increases, the time at which the nearest particle system first hits the empty set increases from logarithmic to exponential depending on the intensity of interaction. In the critical case, the first hitting time is polynomial in the interval length.

Article information

Bernoulli, Volume 12, Number 1 (2006), 101-111.

First available in Project Euclid: 28 February 2006

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

first hitting time nearest particle system


Chen, Dayue; Liu, Juxin; Zhang, Fuxi. The reversible nearest particle system on a finite interval. Bernoulli 12 (2006), no. 1, 101--111.

Export citation


  • [1] Durrett, R. and Liu, X.F. (1988) The contact process on a finite set. Ann. Probab., 16, 1158-1173.
  • [2] Durrett, R. and Schonmann, R.H. (1988) The contact process on a finite set II. Ann. Probab., 16, 1570-1583.
  • [3] Durrett, R., Schonmann, R.H. and Tanaka, N.I. (1989) The contact process on a finite set III: The critical case. Ann. Probab., 17, 1303-1321.
  • [4] Liggett, T.M. (1985) Interacting Particle Systems. New York: Springer-Verlag.
  • [5] Mountford, T.S. (1992) A critical value for the uniform nearest particle system. Ann. Probab., 20, 2031-2042.
  • [6] Mountford, T.S. (2003) Critical reversible attractive nearest particle systems. In E. Merzbach (ed.), Topics in Spatial Stochastic Processes, Lecture Notes in Math. 1802. Berlin: Springer-Verlag.
  • [7] Schinazi, R. (1992) Brownian fluctuations of the edge for critical reversible nearest particle systems. Ann. Probab., 20, 194-205.
  • [8] Wang Z.K. (1980) Birth and Death Processes and Markov Chains (in Chinese). Beijing: Science Publishing House.