Sampling regime

Strongly log-concave + log-smooth

Compare theorems by mathematical guarantee, rate, and source — not by raw crawler rows.

Theorem and frontier cases

best upper · Exact source theorem

Exact ULD / FORS

Theorem 3.2(ii) (High-accuracy simulation of ULD)

Theorem statement

\[\mathsf R_q(\widehat\nu\Vert\pi)\le\delta\]

best lower · Normalized SampleWiki statement

Primary theorem audit pending — this is not presented as a verbatim paper theorem

Complexity / rate

\[\widetilde\Omega(\min\{\sqrt\kappa\log d,d\})\]

upper · Normalized SampleWiki statement

Primary theorem audit pending — this is not presented as a verbatim paper theorem

Guarantee / accuracy

\[\lVert\mu_N-\pi\rVert_{\rm TV}\le\varepsilon\]

Complexity / rate

\[\widetilde O(\kappa\sqrt d\,\operatorname{polylog}(1/\varepsilon))\]

upper · Normalized SampleWiki statement

Primary theorem audit pending — this is not presented as a verbatim paper theorem

Guarantee / accuracy

\[\lVert\mu_N-\pi\rVert_{\rm TV}\le\varepsilon\]

Complexity / rate

\[\widetilde O(\kappa^{5/6}d^{1/3}/\varepsilon^{2/3})\]

upper · Normalized SampleWiki statement

Primary theorem audit pending — this is not presented as a verbatim paper theorem

Guarantee / accuracy

\[\sqrt{\operatorname{KL}}\le\varepsilon\]

Complexity / rate

\[O((d\wedge\sqrt\kappa)\log(d/\varepsilon^2))\]

lower · Normalized SampleWiki statement

Primary theorem audit pending — this is not presented as a verbatim paper theorem

Complexity / rate

\[\widetilde\Omega(\kappa\sqrt d\log(1/\varepsilon))\]