Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Local distortion and µ-mass of the tessels of one dimensional asymptotically optimal quantizers

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Résumé: We consider one dimensional probability distributions $\mu$ with continuous and positive $p.d.f.$ We find the asymptotic of the size and the mass of the Voronoi tessels and we prove that the local distortion associated with stationary or optimal quantizers is asymptotically uniform. Numerical simulations and computations illustrate the theoretical results and lead to the design of some good-fit test for the stationary equilibria.