Gaussian distributions on the space of symmetric positive definite matrices from Souriau's Gibbs state for Siegel domains by coadjoint orbit and moment map

DOI10.1007/978-3-030-80209-7_28zbMath1486.60024OpenAlexW3178846855MaRDI QIDQ2117857

Frédéric Barbaresco

Publication date: 22 March 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-80209-7_28

zbMATH Keywords

symplectic geometrymaximum entropysymmetric positive definite matricesLie groups thermodynamicsexponential density family

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Quadratic and bilinear forms, inner products (15A63) Statistical thermodynamics (82B30) Information geometry (statistical aspects) (62B11)

Cites Work

• On the contraction of the discrete series of \(SU(1,1)\)
• On Gibbs states of mechanical systems with symmetries
• QUANTIZATION IN COMPLEX SYMMETRIC SPACES
• SU(p,q) coherent states and a Gaussian de Finetti theorem
• The contraction of the SU(1,1) discrete series of representations by means of coherent states
• Geometry and dynamics of Gaussian wave packets and their Wigner transforms
• Symplectic Geometry
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