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Asymptotic fluctuations of a particle system with singular interaction

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  • Israelsson, Stefan

Abstract

A particle system on the real line with singular interaction consisting of electrostatic repulsion and a linear restoring force is considered. The empirical measure process is known to converge weakly in a space of continuous-measure-valued functions. In this work we show that the fluctuations around the limiting process, appropriately scaled, converge weakly to a Gaussian-distribution-valued process.

Suggested Citation

  • Israelsson, Stefan, 2001. "Asymptotic fluctuations of a particle system with singular interaction," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 25-56, May.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:1:p:25-56
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    Cited by:

    1. Unterberger, Jérémie, 2018. "Global fluctuations for 1D log-gas dynamics," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4104-4153.
    2. Bender, Martin, 2008. "Global fluctuations in general [beta] Dyson's Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1022-1042, June.

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