A Gradient Flow Approach to Quantization of Measures

Abstract : In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$ , we find a continuous version of it that corresponds to the limit as the number of particles tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence result for the discrete and continuous dynamics.
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Submitted on : Sunday, January 25, 2015 - 4:58:18 PM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
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Emanuele Caglioti, François Golse, Mikaela Iacobelli. A Gradient Flow Approach to Quantization of Measures. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2015, 25 (10), pp.1845-1885. ⟨10.1142/S0218202515500475⟩. ⟨hal-01109228⟩

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