The HK-Boltzmann gradient flow preserves Gaussianity, and the reduced equations for mean, covariance, and mass admit exponential convergence rates with explicit dependence on the geometry parameters.
Evolutionary Variational Inequalities on the Hellinger-Kantorovich and Spherical Hellinger-Kantorovich spaces
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abstract
We study the minimizing movement scheme for families of geodesically semi-convex functionals defined on either the Hellinger-Kantorovich or the Spherical Hellinger-Kantorovich space. By exploiting some of the finer geometric properties of those spaces, we prove that the sequence of curves, which are produced by geodesically interpolating the points generated by the minimizing movement scheme, converges to curves that satisfy the Evolutionary Variational Inequality (EVI), when the time step goes to 0.
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Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow
The HK-Boltzmann gradient flow preserves Gaussianity, and the reduced equations for mean, covariance, and mass admit exponential convergence rates with explicit dependence on the geometry parameters.