An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture
Publication
, Journal Article
Chen, Y
November 27, 2020
We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $d^{-o_d(1)}$. When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $d^{-1/4}$. Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain's slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concave measures and better mixing time bounds for MCMC sampling algorithms on log-concave measures.
Duke Scholars
Publication Date
November 27, 2020
Citation
APA
Chicago
ICMJE
MLA
NLM
Chen, Yuansi. “An Almost Constant Lower Bound of the Isoperimetric Coefficient in the
KLS Conjecture,” November 27, 2020.
Chen Y. An Almost Constant Lower Bound of the Isoperimetric Coefficient in the
KLS Conjecture. 2020 Nov 27;
Chen, Yuansi. An Almost Constant Lower Bound of the Isoperimetric Coefficient in the
KLS Conjecture. Nov. 2020.
Chen Y. An Almost Constant Lower Bound of the Isoperimetric Coefficient in the
KLS Conjecture. 2020 Nov 27;
Publication Date
November 27, 2020