The Speed of Convergence with respect to the Kolmogorov-Smirnov Metric in the Soshnikov Central Limit Theorem for the Sine-Process
Abstract
For rescaled additive functionals of the sine-process, upper bounds are obtained for their speed of convergence to the Gaussian distribution with respect to the Kolmogorov-Smirnov metric. Under scaling with coefficient R the Kolmogorov-Smirnov distance is bounded from above by c/ R for a smooth function and by c/R for a function holomorphic in a horizontal strip.
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