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• W2963669832 abstract "We consider the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, [ dlambda _t^i=frac{1} {sqrt{N} } dW_t^i - V'(lambda _t^i) dt+ frac{beta } {2N} sum _{jnot =i} frac{dt} {lambda ^i_t-lambda ^j_t}, qquad i=1,ldots ,N, qquad mbox{(0.1)} ] with $beta >1$, 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 $beta $-ensemble, with sufficiently regular convex potential $V$. The limit $Nto infty $ is known to satisfy a mean-field Mc Kean-Vlasov equation. Fluctuations around this limit have been shown [39] to define a Gaussian process solving some explicit martingale problem written in terms of a generalized transport equation. We prove a series of results concerning either the Mc Kean-Vlasov equation for the density $rho _t$, notably regularity results and time-evolution of the support, or the associated hydrodynamic fluctuation process, whose space-time covariance kernel we compute explicitly." @default.
• W2963669832 created "2019-07-30" @default.
• W2963669832 creator A5064220738 @default.
• W2963669832 date "2019-01-01" @default.
• W2963669832 modified "2023-10-15" @default.
• W2963669832 title "Global fluctuations for 1D log-gas dynamics. Covariance kernel and support" @default.
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• W2963669832 doi "https://doi.org/10.1214/19-ejp288" @default.
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