Densities of generalized stochastic areas and windings arising from Anti-de Sitter and Hopf fibrations
Densities of generalized stochastic areas and windings arising from Anti-de Sitter and Hopf fibrations
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由反德西特和霍普夫纤维引起的广义随机区域和绕组的密度
DOI：
10.1016/j.indag.2019.12.005
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
N. Demni
中科院分区：
文献类型：
--
作者：
N. Demni
在本文的第一部分，我们得到了广义随机区域的半群密度的显式表达式，这些半群密度是由Anti-de Sitter和Hopf颤动引起的。受Heisenberg群与Dirichlet级数之间的数论联系的启发，我们将对应于一维Anti de Sitter纤维的广义随机区域的Mellin变换表示为一系列计算为整数的Riemann Zeta函数。在本文的第二部分，我们得到了Poincaré圆盘和复射影直线上绕原点的缠绕过程的固定时间边际密度。
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 derive fixed-time marginal densities of winding processes around the origin in the Poincaré disc and in the complex projective line.