A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Equipped with the L^2-distortion distance, the space "X" of all metric measure spaces (X,d,m) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on "X" are presented.
Given a real-valued function c defined on the cartesian product of a generic Carnot group $\G$ and the first layer V1 of its Lie algebra, we introduce a notion of c horizontal convex (c H-convex) function on $\G$ as the supremum of a suitable family of affine functions; this family is defined pointwisely, and …
We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients, whose properties are remarkably different with respect to the Riemannian case. As …
Study on Wasserstein gradient flow of MMD with nonsmooth energy kernels in various dimensions.
problem Analyzing the Wasserstein gradient flow of Maximum Mean Discrepancy with energy kernels in different dimensions.
method Global well-posedness proof for probability densities in subcritical L^p spaces, N-particle system convergence, and construction of collision-free saddle equilibria.
result Global well-posedness and convergence results for the MMD flow in various dimensions and particle systems.