The Speed of Convergence with respect to the Kolmogorov-Smirnov Metric in the Soshnikov Central Limit Theorem for the Sine-Process
arXiv:2412.20910
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 the Kolmogorov-Smirnov distance is bounded from above by for a smooth function and by for a function holomorphic in a horizontal strip.
4 pages