| Abstract: |
| We study statistical models for multivariate extremes based on transport to a center-outward reference distribution. Our approach combines optimal-transport-based and flow-matching ideas to learn distributional structure in the bulk while retaining geometric features of the tail. In particular, transport to a product-uniform reference provides a natural way to encode radial and angular extremal behaviour, and to examine how inverse rays and transport contours reflect tail geometry. We discuss both Brenier-type and entropic regularizations, with emphasis on the trade-off between smoothness, invertibility, and fidelity in the extremes. The resulting perspective points toward a broader connection between multivariate regular variation, geometric extreme-value analysis, and modern generative modeling.We introduce geometric extremal graphical models, a new framework for describing dependence in multivariate extreme events. The approach is based on a geometric representation of the limiting behaviour of suitably scaled random vectors with light-tailed margins. For block graphs, we show how different measures of extremal dependence propagate through the graph. We focus in particular on measures connected to conditional extreme value theory, which are useful when extreme events occur in some variables without requiring all variables to be extreme at the same time. We also discuss the case of joint extreme behaviour, where several variables become extreme together. Together with recent work linking geometric ideas in multivariate extremes to practical statistical models, these results open the way to modelling high-dimensional extremes with complex dependence structures. |
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