Global fluctuations for 1D log-gas dynamics

Jérémie Unterberger

Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4104-4153

Abstract: We study in this article the hydrodynamic limit in themacroscopic regime of the coupled system of stochastic differential equations, (0.1)dλti=1NdWti−V′(λti)dt+β2N∑j≠idtλti−λtj,i=1,…,N,with β>1, sometimes called generalized Dyson’s Brownian motion, describing the dissipative dynamics of a log-gas of N equal charges with equilibrium measure corresponding to a β-ensemble, with sufficiently regular convex potential V. The limit N→∞ is known to satisfy a mean-field Mc-Kean–Vlasov equation. We prove that, for suitable initial conditions, fluctuations around the limit are Gaussian and satisfy an explicit PDE.

Keywords: Random matrices; Dyson’s Brownian motion; Log-gas; Beta-ensembles; Hydrodynamic limit; Stieltjes transform; Entropy (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:12:p:4104-4153

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DOI: 10.1016/j.spa.2018.01.008

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