论文标题
限制$ \ ell_p^n $ -balls的小编织随机部分的卷定理
Limit theorems for the volumes of small codimensional random sections of $\ell_p^n$-balls
论文作者
论文摘要
我们为$ b_ {p}^n $（$ \ ell_p^n $的单位球）建立了中央限制定理，该交叉点具有均匀的codimension $ d $的均匀随机子空间，用于固定$ d $和$ n \ to \ infty $。作为推论，我们获得了预期体积的更高阶近似值，从而完善了Koldobsky和Lifschitz的先前结果，并从Eldan-Klartag版本获得的CLT获得了凸体的近似值。我们还获得了$ b_p^n $的Minkowski功能的中心限制定理，该功能在单位球体上均匀分布的随机矢量进行了评估。
We establish Central Limit Theorems for the volumes of intersections of $B_{p}^n$ (the unit ball of $\ell_p^n$) with uniform random subspaces of codimension $d$ for fixed $d$ and $n\to \infty$. As a corollary we obtain higher order approximations for expected volumes, refining previous results by Koldobsky and Lifschitz and approximations obtained from the Eldan--Klartag version of CLT for convex bodies. We also obtain a Central Limit Theorem for the Minkowski functional of the intersection body of $B_p^n$, evaluated on a random vector distributed uniformly on the unit sphere.
