Probability Seminar

Central limit theorems on stratified spaces

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Speaker(s): Ezra Miller (Duke University, Mathematics)
This talk summarizes geometry and probability of central limit theorems (CLTs) for Fréchet means on singular spaces. It begins with what it means to stratify a singular space by subspaces that are manifolds, and what the geometry of logarithm maps looks like in such spaces. Since geometric versions of the CLT naturally concern tangent vectors, the next step is to define random tangent fields. Tangential collapse then pushes the singular picture into a vector space, which allows Gaussians on singular spaces to be defined. These are then related to escape vectors (singular versions of influence functions), which give rise to assorted CLT statements, in geometric form or as solutions to random variational problems. The talk is based on a series of four papers https://arxiv.org/abs/2311.09451 https://arxiv.org/abs/2311.09453 https://arxiv.org/abs/2311.09454 https://arxiv.org/abs/2311.09455 joint with Jonathan Mattingly and Do Tran.

Physics 119