3 problems

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Limit formula for exactly $L^r$ -optimal quantizers
Exact-optimality conjecture. For sequences $(\alpha_n)$ of exactly $L^r$ -optimal $n$ -quantizers, this limiting result holds true, namely
Conjectureopenasymptotic-analysis optimal-quantizers quantizationarXiv posted 2 days ago
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Sharp lower-bound rate for asymptotically $L^r$ -optimal quantizers
Let $(\alpha_n)_{n\ge 1}$ be an $L^r$ -rate-optimal sequence of $n$ -quantizers for a probability measure $P$ , and consider the lower bound for its $L^s(P)$ -quantization rate of conv…
Conjectureopenoptimal-quantizers probability-measures quantizationarXiv posted 2 days ago
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Roychowdhury's conjecture on two-means for the uniform distribution on a disc
Roychowdhury's conjecture. The Voronoi regions of the points in an optimal set of two-means partition the disc into two semicircles.
Conjectureopengeometric-probability optimal-quantizers quantization-theoryarXiv posted 2 days ago

Limit formula for exactly LrL^rLr-optimal quantizers