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.

45 pages, no figure

Cited by in corpus (5)

• Semi-discrete unbalanced optimal transport and quantization
• Weighted ultrafast diffusion equations: from well-posedness to long-time behaviour
• Quantization of Measures and Gradient Flows: a Perturbative Approach in the 2-Dimensional Case
• Asymptotic quantization on Riemannian manifolds via covering growth estimates
• Asymptotics of the quantization problem on metric measure spaces