Exponential-wrapped distributions on SL(2, C) and the Möbius group

Emmanuel Chevallier (1)

1 FRESNEL - Institut FRESNEL

In this paper we discuss the construction of probability distributions on the group SL(2, C) and the Möbius group using the exponential map. In particular, we describe the injectivity and surjectivity domains of the exponential map and provide its Jacobian determinant. We also show that on SL(2, C) and the Möbius group, there are no isotropic densities in the group sense.

Mots clés: statistics on Lie groups; exponential map; wrapped distributions; Killing form

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie [stat.TH]; Géométrie différentielle [math.DG]

Emmanuel Chevallier. Exponential-wrapped distributions on SL(2, C) and the Möbius group. Lecture Notes in Computer Science, 12829, pp.265, 2021, ⟨10.1007/978-3-030-80209-7_30⟩. ⟨hal-03463991⟩