Foundations of Quantization for Probability Distributions
Graf & Luschgy (2000, 2002)
- Use
nearest published instance of a uniform LLN over Voronoi-type partition classes (DS14 Step 3 companion to C1) and of existence/stationarity machinery for population quantizers. Thm 4.1/4.2 (secondary-verified via Levrard and Liu–Pagès): every cell of an optimal quantizer carries positive mass with null overlaps — the population (M2) analogue on the distortion side, and the deletion-vs- mechanism reused in DS15's rigidity lemma. Thm 5.1: scalar log-concave uniqueness (the book anchor for DS15's assumption (S)).
- Does not transfer
the whole framework is additive per-point distortion; no result covers a global nonlinear matrix functional of cell moments.
- Papers
Foundations of Quantization for Probability Distributions (Springer LNM 1730; Ch. 4 existence/stationarity of optimal quantizers under moment conditions); Rates of convergence for the empirical quantization error (Ann. Probab. 30:874–897; bracketing-entropy uniform LLN over Voronoi-cell indicator classes).
Springer LNM 1730. Every cell of an optimal quantizer has positive mass and null boundaries (content secondary-verified via Roychowdhury Prop 1.1 and Liu-Pages 2020, who pin the null-boundary statement to Thm 4.2 and existence to Thm 4.12; the "Thm 4.1" numbering for positive mass is unverified - 30 Aug 2026 audit); Thm 5.1: uniqueness of the scalar log-concave K-quantizer (numbering and content confirmed twice at secondary level).
Cited by
- Publication-grade audit of the DS15 margins dichotomyAUDIT-DS-MARGINS-AT-OPTIMA
- Exact off-class global basin transfers to empirical exchange-stable optimaDS-NONCENTERED-GLOBAL-BASIN-TRANSFER
- Margin price and value funnel at arbitrary finite Ds labelingsDS-STABLE-MARGINS-PRICE
- Margins dichotomy at global finite Ds optima (conditionally centered laws, scalar nuisance)OPEN-DS-MARGINS-AT-OPTIMA
Relevant to
Claims this source bears on without being cited in their proofs.