# Stochastic areas, winding numbers and Hopf fibrations

@article{Baudoin2016StochasticAW, title={Stochastic areas, winding numbers and Hopf fibrations}, author={Fabrice Baudoin and Jing Wang}, journal={Probability Theory and Related Fields}, year={2016}, volume={169}, pages={977-1005} }

We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces $$\mathbb {CP}^n$$CPn and $$\mathbb {CH}^n$$CHn. The characteristic functions of those processes are computed and limit theorems are obtained. In the case $$n=1$$n=1, we also study windings of the Brownian motion on those spaces and compute the limit distributions. For $$\mathbb {CP}^n$$CPn the geometry of the Hopf fibration plays a central role, whereas for $$\mathbb {CH}^n$$CHn it…

## 16 Citations

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We study the stochastic processes that are images of Brownian motions on Heisenberg group H2n+1 under conformal maps. In particular, we obtain that Cayley transform maps Brownian paths in H2n+1 to a…

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We study several matrix diffusion processes constructed from a unitary Brownian motion. In particular, we use the Stiefel fibration to lift the Brownian motion of the complex Grassmannian to the…

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ABSTRACT We identify the short time asymptotics of the sub-Riemannian heat content for a smoothly bounded domain in the first Heisenberg group. Our asymptotic formula generalizes prior work by van…

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