Applications of optimal transport to Dyson Brownian Motions and beyond
Abstract
We develop a new method based on Caffarelli's contraction theorem in optimal transport to obtain sharp and uniform modulus of continuity estimates for β-Dyson Brownian motions with β ≥ 2. Our method extends to a large class of random curve collections, which can be viewed as log-concave perturbations of Brownian motions, including the β-Dyson Brownian motion, the Airyβ line ensemble, the KPZ line ensemble, and the O'Connell-Yor line ensemble.
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