Areas on the space of smooth probability density functions on S^2

10/14/2021

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by   J. C. Ruíz-Pantaleón, et al.

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We present symbolic and numerical methods for computing Poisson brackets on the spaces of measures with positive densities of the plane, the 2-torus, and the 2-sphere. We apply our methods to compute symplectic areas of finite regions for the case of the 2-sphere, including an explicit example for Gaussian measures with positive densities.