A stochastic algorithm finding generalized means on compact manifolds

The algorithm is fed sequentially with independent random variables (Yn)n∈N distributed according to ν and this is the only knowledge of ν required. It evolves like a Brownian motion between the times it jumps in the direction of the Yn. Its principle is based on simulated annealing and homogenization, so that temperature and approximation schemes must be tuned up. The proof relies on the investigation of the evolution of a time-inhomogeneous L2 functional and on the corresponding spectral gap estimates due to Holley, Kusuoka and Stroock.