  The monograph is devoted to the study of stochastic area functionals of
Brownian motions and of the associated heat kernels on Lie groups and
Riemannian manifolds. It is essentially self-contained and as such can serve as
a textbook on the theory of Brownian motions and horizontal Brownian motions on
manifolds. Emphasis is put on concrete examples which allows us to concretely
illustrate the rich and deep interactions between stochastic calculus,
Riemannian and sub-Riemannian geometry, the theory of complex and quaternionic
symmetric spaces and random matrices.

Probability;Differential Geometry