Summary
We study a one-dimensional semi-infinite system of identical particles, driven by a constant force acting only on the first particle. Particles interact through elastic collisions. At time zero all particles are at rest, and the interparticle distances are i.i.d. r.v.'s, the support of the distribution being in (d, ∞), d>0. We show that if d is large enough the dynamics has a strong cluster property, and prove, for large times, convergence to a limiting distribution for the system as seen from the first particle, as well as existence of drift velocity and invariance principle for the motion of the first particle.
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Partially supported by C.N.R.-C.N.Pq. agreement
Partially supported by M.P.I. research funds
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Boldrighini, C., Cosimi, G.C., Frigio, S. et al. Convergence to a stationary state and diffusion for a charged particle in a standing medium. Probab. Th. Rel. Fields 80, 481–500 (1989). https://doi.org/10.1007/BF00318904
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DOI: https://doi.org/10.1007/BF00318904
Keywords
- Stochastic Process
- Stationary State
- Charged Particle
- Probability Theory
- Statistical Theory