The Annals of Probability

Uniqueness of the Tagged Particle Process in a System with Local Interactions

Ilie Grigorescu

Full-text: Open access

Abstract

It has been shown that for a system of Brownian motions with local interaction considered in a diffusive scaling, under some regularity assumptions on the initial profile, the tagged particle process converges to a diffusion. We provide a sufficient condition for granting both the existence and the uniqueness of the tagged particle process for an arbitrary initial profile.

Article information

Source
Ann. Probab., Volume 27, Number 3 (1999), 1268-1282.

Dates
First available in Project Euclid: 29 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022677446

Digital Object Identifier
doi:10.1214/aop/1022677446

Mathematical Reviews number (MathSciNet)
MR1733147

Zentralblatt MATH identifier
0961.60100

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 82C05

Keywords
Tagged particle interacting diffusions arbitrary initial profile

Citation

Grigorescu, Ilie. Uniqueness of the Tagged Particle Process in a System with Local Interactions. Ann. Probab. 27 (1999), no. 3, 1268--1282. doi:10.1214/aop/1022677446. https://projecteuclid.org/euclid.aop/1022677446


Export citation

References

  • 1 GRIGORESCU, I. 1999. Self-diffusion for Brownian motions with local interaction. Ann. Probab. 27 1208 1267.
  • 2 GUO, M.1984. Limit theorems for interacting particle systems. New York University.
  • 3 GUO, M.and PAPANICOLAOU, G. 1985. Self-diffusion of interacting Brownian particles. In Probabilistic Methods in Mathematical Physics 113 151. Katata, Kyoto, Japan.
  • 4 VARADHAN, S. R. S. 1991. Scaling limits for interacting diffusions. Comm. Math. Phys. 135 313 353.
  • SALT LAKE CITY, UTAH 84112-0090