A gradient flow approach to quantization of measures

Authors :: Mikaela Iacobelli
François Golse
Emanuele Caglioti
Dipartimento di Matematica 'Guido Castelnuovo' [Roma I] (Sapienza University of Rome)
Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome]
Centre de Mathématiques Laurent Schwartz (CMLS)
Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
Source :: Mathematical Models and Methods in Applied Sciences, Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2015, 25 (10), pp.1845-1885. ⟨10.1142/S0218202515500475⟩
Publication Year :: 2015
Publisher :: World Scientific Pub Co Pte Lt, 2015.
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.<br />45 pages, no figure