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Conditional principles for random weighted measures

Nathael Gozlan — 2005

ESAIM: Probability and Statistics

In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form L n = 1 n i = 1 n Z i δ x i n , ( Z i ) i being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.

Poincaré inequalities and dimension free concentration of measure

Nathael Gozlan — 2010

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we consider Poincaré inequalities for non-euclidean metrics on ℝ. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and inf-convolution inequalities. Workable sufficient conditions are given...

Conditional principles for random weighted measures

Nathael Gozlan — 2010

ESAIM: Probability and Statistics

In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form L n = 1 n i = 1 n Z i δ x i n , ( being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.

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