A gradient flow approach to quantization of measures
  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. 
Emanuele Caglioti, Fran\c{c}ois Golse, Mikaela Iacobelli
math.AP