2019/04/13 by Nizar Demni, Demni, Nizar
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1904.06510
openalex publication_date 2019/04/13 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28
In the first part of this paper, we derive explicit expressions of the semi-group densities of generalized stochastic areas arising from the Anti-de Sitter and the Hopf fibrations. Motivated by the number-theoretical connection between the Heisenberg group and Dirichlet series, we express the Mellin transform of the generalized stochastic area corresponding to the one-dimensional Anti de Sitter fibration as a series of Riemann Zeta function evaluated at integers. In the second part of the paper, we focus on winding processes around the origin in the Poincaré disc and in the complex projective line. More pricesely, we derive the fixed-time marginal density of the former process while we give a ultraspherical series expansion of the characteristic function of the latter.