论文标题
KLS猜想中等值系数的几乎恒定的下限
An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture
论文作者
论文摘要
我们证明了KLS猜想中等级系数的几乎恒定的下限。下限具有尺寸依赖关系$ d^{ - o_d（1）} $。当尺寸足够大时，我们的下限比具有尺寸依赖关系$ d^{ - 1/4} $的先前最佳界限更紧。 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.
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.
