Student Probability Seminar

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Asymptotics of Wasserstein distances under Gaussian smoothing

Speaker: Hong-Bin Chen, CIMS

Location: Online

Date: Wednesday, February 24, 2021, 9 a.m.

Notes:

We start by reviewing basics about Wasserstein distances on probability measures and famous results on the contraction of Wasserstein distances when measures are evolved by heat semigroups on curved spaces. Then, we consider the contraction on flat Euclidean spaces where the heat semigroup is given by Gaussian convolutions. We will state a few results on the asymptotics and give a sketch of proof involving Hermite polynomials.