分野別セミナー

We consider rate of convergence in the Kolmogorov distance between a distribution of renormalized sample maximum and the classical or free extreme value distribution. Barbour and Chen (2005), Chen et al. (2011) and Kusumoto and Takeuchi (2020) have already obtained the results on classical extreme value distributions. A crucial point to study them is to use the Stein’s method. A purpose in this talk is to provide rate of convergence to free extreme value distribution via the Stein’s method. This presentation is organized as follows: The first part is to introduce the free extreme value distributions. In the next part, we establish the Stein type differential operator which is characterized by the free extreme value distribution and provide rate of convergence towards the free extreme value distribution.