| Abstract
| - Let M be a complete Riemannian manifold, M ∈ ℕ and p ≥ 1 . We prove that almost everywhere on x = ( x1, ..., xN) ∈ MN for Lebesgue measure in MN, the measure \hbox{$\di \mu(x)=\f1N\sum_{k=1}^N\d_{x_k}$} has a unique p-mean ep( x) . As a consequence, if X = ( X1, ..., XN) is a MN-valued random variable with absolutely continuous law, then almost surely μ( X( ω)) has a unique p-mean. In particular if ( Xn) n ≥ 1 is an independent sample of an absolutely continuous law in M, then the process ep,n( ω) = ep( X1( ω), ..., Xn( ω)) is well-defined. Assume M is compact and consider a probability measure ν in M. Using partial simulated annealing, we define a continuous semimartingale which converges in probability to the set of minimizers of the integral of distance at power p with respect to ν. When the set is a singleton, it converges to the p-mean.
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