Limit Distribution of Componentwise Maxima: Proof of Theorem 28

This lecture discusses the limit distribution of componentwise maxima of independent random variables, leading to a non-degenerate distribution with unit Fréchet margins. The proof involves linear renormalization and angular distribution considerations, demonstrating the convergence to a random variable Z. The lecture explores the implications of linear transformations and monotone functions for different dimensions, ensuring unit Fréchet limiting distributions. The angular variable W is crucial in understanding the joint limiting distribution of the vectors. The lecture concludes with a detailed analysis of the Laplace functional and the Poisson process induced by the transformations.