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.
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Communicated by J. L. Lebowitz
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Spohn, H. Equilibrium fluctuations for interacting Brownian particles. Commun.Math. Phys. 103, 1–33 (1986). https://doi.org/10.1007/BF01464280
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DOI: https://doi.org/10.1007/BF01464280