The log-gas partition function is uniformly bounded in N for arbitrary bounded base measures, giving a mean-field convergence rate of order 1/N instead of (log N)/N for repulsive logarithmic interactions.
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Sharp mean-field estimates for the repulsive log gas in any dimension
The log-gas partition function is uniformly bounded in N for arbitrary bounded base measures, giving a mean-field convergence rate of order 1/N instead of (log N)/N for repulsive logarithmic interactions.