Equilibrium fluctuations for interacting Brownian particles View Full Text


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Article Info

DATE

1986-03

AUTHORS

Herbert Spohn

ABSTRACT

We consider an infinitely extended system of Brownian particles interacting by a pair force-gradV. Their initial distribution is stationary and given by the Gibbs measure associated with the potentialV with fugacityz. We assume thatV is symmetric, finite range, three times continuously differentiable, superstable, and positive and that the fugacity is small in the sense that 0≦z≦0.28/eεdq(1-e−V(q)). In addition a certain essential self-adjointness property is assumed. We prove then that the time-dependent fluctuations in the density on a spatial scale of order ɛ−1 and on a time scale of order ɛ−2 converge as ɛ→0 to a Gaussian field with covariance χεdqg(q)(e(ρ/2χ)Δ|t|f)(q) withp the density and χ the compressibility. More... »

PAGES

1-33

References to SciGraph publications

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  • 1983-11. Analyticity for one-dimensional systems with long-range superstable interactions in JOURNAL OF STATISTICAL PHYSICS
  • 1977-03. Unendlich-dimensionale Wienerprozesse mit Wechselwirkung in PROBABILITY THEORY AND RELATED FIELDS
  • 1983. Hydrodynamik gekoppelter diffusionen: Fluktuationen im gleichgewicht in DYNAMICS AND PROCESSES
  • 1980. Non-equilibrium solutions of an infinite system of stochastic differential equations in STOCHASTIC DIFFERENTIAL SYSTEMS FILTERING AND CONTROL
  • 1979. Canonical Gibbs Measures, Some Extensions of de Finetti's Representation Theorem for Interacting Particle Systems in NONE
  • 1974-06. On the local central limit theorem for Gibbs processes in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1983-09. Scaling limit of some critical models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1968-09. On the mechanical equilibrium equations for classical systems in IL NUOVO CIMENTO B (1965-1970)
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    http://scigraph.springernature.com/pub.10.1007/bf01464280

    DOI

    http://dx.doi.org/10.1007/bf01464280

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    https://app.dimensions.ai/details/publication/pub.1001060784


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