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global differential calculus 1levi-civita connection 1optimal transport 1otto metric 1riemannian geometry 1wasserstein spaces 1

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math.PR2025

Massive Particle Systems, Wasserstein Brownian Motions, and the Dean-Kawasaki Equation

Lorenzo Dello Schiavo

We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and…

math.PR2025

Ill-posedness of the pure-noise Dean-Kawasaki equation

Lorenzo Dello Schiavo, Vitalii Konarovskyi

We prove that the Dean-Kawasaki-type stochastic partial differential equation with vector-valu…

math.PR2024

Conformally invariant random fields, quantum Liouville measures, and random Paneitz operators on Riemannian manifolds of even dimension

Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer +1

For large classes of even-dimensional Riemannian manifolds , we construct and analyze conformally invariant random fields. These centered Gaussian fields , called co-…