Quaternionic Brownian Windings

Explore the intricacies of quaternionic Brownian windings in this 58-minute lecture by Fabrice BAUDOIN from the University of Connecticut. Delve into topics such as the Lévy area formula, Brownian motion in complex projective space, stochastic area in CP and CH, skew-product decomposition, and asymptotic Brownian winding. Gain insights into the complex hyperbolic space and limit distribution as part of the School and Workshop on Mixing and Control series presented by ICTP Mathematics.

Intro
The Lévy area formula
The Levy area formula
The complex projective space CP
Brownian motion in CP
Stochastic area in CP
Skew-product decomposition
Limit distribution
The complex hyperbolic space
Stochastic area in CH
Skew product decomposition
Winding form
Asymptotic Brownian Winding