Matches in SemOpenAlex for { <https://semopenalex.org/work/W2912153643> ?p ?o ?g. }
- W2912153643 abstract "We show that the Cheeger constant for $n$-dimensional isotropic logconcave measures is $O(n^{1/4})$, improving on the previous best bound of $O(n^{1/3}sqrt{log n}).$ As corollaries we obtain the same improved bound on the thin-shell estimate, Poincare constant and Lipschitz concentration constant and an alternative proof of this bound for the isotropic (slicing) constant; it also follows that the ball walk for sampling from an isotropic logconcave density in ${bf R}^{n}$ converges in $O^{*}(n^{2.5})$ steps from a warm start. The proof is based on gradually transforming any logconcave density to one that has a significant Gaussian factor via a Martingale process. Extending this proof technique, we prove that the log-Sobolev constant of any isotropic logconcave density in ${bf R}^{n}$ with support of diameter $D$ is $Omega(1/D)$, resolving a question posed by Frieze and Kannan in 1997. This is asymptotically the best possible estimate and improves on the previous bound of $Omega(1/D^{2})$ by Kannan-Lovasz-Montenegro. It follows that for any isotropic logconcave density, the ball walk with step size $delta=Theta(1/sqrt{n})$ mixes in $Oleft(n^{2}Dright)$ proper steps from emph{any }starting point. This improves on the previous best bound of $O(n^{2}D^{2})$ and is also asymptotically tight. The new bound leads to the following large deviation inequality for an $L$-Lipschitz function $g$ over an isotropic logconcave density $p$: for any $t>0$, [ Pr_{xsim p}left(left|g(x)-bar{g}right|geq Lcdot tright)leqexp(-frac{ccdot t^{2}}{t+sqrt{n}}) ] where $bar{g}$ is the median or mean of $g$ for $xsim p$; this generalizes and improves on previous bounds by Paouris and by Guedon-Milman. The technique also bounds the ``small ball'' probability in terms of the Cheeger constant, and recovers the current best bound." @default.
- W2912153643 created "2019-02-21" @default.
- W2912153643 creator A5024980585 @default.
- W2912153643 creator A5085424042 @default.
- W2912153643 date "2016-12-05" @default.
- W2912153643 modified "2023-10-18" @default.
- W2912153643 title "Eldan's Stochastic Localization and the KLS Conjecture: Isoperimetry, Concentration and Mixing" @default.
- W2912153643 cites W100944330 @default.
- W2912153643 cites W1521305480 @default.
- W2912153643 cites W1559116151 @default.
- W2912153643 cites W1800323139 @default.
- W2912153643 cites W1858644816 @default.
- W2912153643 cites W1996999318 @default.
- W2912153643 cites W2011049178 @default.
- W2912153643 cites W2015846973 @default.
- W2912153643 cites W2024939087 @default.
- W2912153643 cites W2025334959 @default.
- W2912153643 cites W2028104836 @default.
- W2912153643 cites W2028816357 @default.
- W2912153643 cites W2030644212 @default.
- W2912153643 cites W2041990574 @default.
- W2912153643 cites W2049731483 @default.
- W2912153643 cites W2049825392 @default.
- W2912153643 cites W2051997748 @default.
- W2912153643 cites W2077458243 @default.
- W2912153643 cites W2077810240 @default.
- W2912153643 cites W2087867172 @default.
- W2912153643 cites W2089673856 @default.
- W2912153643 cites W2098571881 @default.
- W2912153643 cites W2108906300 @default.
- W2912153643 cites W2109970935 @default.
- W2912153643 cites W2128585485 @default.
- W2912153643 cites W2152898676 @default.
- W2912153643 cites W2159000620 @default.
- W2912153643 cites W2170316986 @default.
- W2912153643 cites W2221136013 @default.
- W2912153643 cites W2314241212 @default.
- W2912153643 cites W2344066978 @default.
- W2912153643 cites W24149473 @default.
- W2912153643 cites W2562438252 @default.
- W2912153643 cites W2594480752 @default.
- W2912153643 cites W2963378877 @default.
- W2912153643 cites W2963841171 @default.
- W2912153643 cites W3099857106 @default.
- W2912153643 cites W88155604 @default.
- W2912153643 cites W934596661 @default.
- W2912153643 hasPublicationYear "2016" @default.
- W2912153643 type Work @default.
- W2912153643 sameAs 2912153643 @default.
- W2912153643 citedByCount "2" @default.
- W2912153643 countsByYear W29121536432019 @default.
- W2912153643 countsByYear W29121536432021 @default.
- W2912153643 crossrefType "posted-content" @default.
- W2912153643 hasAuthorship W2912153643A5024980585 @default.
- W2912153643 hasAuthorship W2912153643A5085424042 @default.
- W2912153643 hasConcept C114614502 @default.
- W2912153643 hasConcept C121332964 @default.
- W2912153643 hasConcept C122041747 @default.
- W2912153643 hasConcept C134306372 @default.
- W2912153643 hasConcept C138885662 @default.
- W2912153643 hasConcept C184050105 @default.
- W2912153643 hasConcept C199360897 @default.
- W2912153643 hasConcept C22324862 @default.
- W2912153643 hasConcept C2777027219 @default.
- W2912153643 hasConcept C2779557605 @default.
- W2912153643 hasConcept C2780388253 @default.
- W2912153643 hasConcept C2780990831 @default.
- W2912153643 hasConcept C33923547 @default.
- W2912153643 hasConcept C41008148 @default.
- W2912153643 hasConcept C41895202 @default.
- W2912153643 hasConcept C62520636 @default.
- W2912153643 hasConcept C77553402 @default.
- W2912153643 hasConceptScore W2912153643C114614502 @default.
- W2912153643 hasConceptScore W2912153643C121332964 @default.
- W2912153643 hasConceptScore W2912153643C122041747 @default.
- W2912153643 hasConceptScore W2912153643C134306372 @default.
- W2912153643 hasConceptScore W2912153643C138885662 @default.
- W2912153643 hasConceptScore W2912153643C184050105 @default.
- W2912153643 hasConceptScore W2912153643C199360897 @default.
- W2912153643 hasConceptScore W2912153643C22324862 @default.
- W2912153643 hasConceptScore W2912153643C2777027219 @default.
- W2912153643 hasConceptScore W2912153643C2779557605 @default.
- W2912153643 hasConceptScore W2912153643C2780388253 @default.
- W2912153643 hasConceptScore W2912153643C2780990831 @default.
- W2912153643 hasConceptScore W2912153643C33923547 @default.
- W2912153643 hasConceptScore W2912153643C41008148 @default.
- W2912153643 hasConceptScore W2912153643C41895202 @default.
- W2912153643 hasConceptScore W2912153643C62520636 @default.
- W2912153643 hasConceptScore W2912153643C77553402 @default.
- W2912153643 hasLocation W29121536431 @default.
- W2912153643 hasOpenAccess W2912153643 @default.
- W2912153643 hasPrimaryLocation W29121536431 @default.
- W2912153643 hasRelatedWork W1451577772 @default.
- W2912153643 hasRelatedWork W1512648280 @default.
- W2912153643 hasRelatedWork W185291893 @default.
- W2912153643 hasRelatedWork W1989800311 @default.
- W2912153643 hasRelatedWork W1997081654 @default.
- W2912153643 hasRelatedWork W2012667816 @default.
- W2912153643 hasRelatedWork W2461348257 @default.
- W2912153643 hasRelatedWork W2766774978 @default.