论文标题
随机整数凸面的预期平均宽度
Expected mean width of the randomized integer convex hull
论文作者
论文摘要
令$ k \ in \ r^d $为凸板，并假设$ l $是一个随机旋转和移动的整数晶格。令$ k_l $为（随机）点$ k \ cap l $的凸壳。研究了$ k_l $的平均宽度$ W（k_l）$。平均宽度差的渐近顺序$ w（ł）-w（（（（olk）_l）$）$最大化了由多面体获得的订单，并将平滑凸组的订单最小化为$ \ \ \ \ \ \ \ to \ iffty $。
Let $K \in \R^d$ be a convex body, and assume that $L$ is a randomly rotated and shifted integer lattice. Let $K_L$ be the convex hull of the (random) points $K \cap L$. The mean width $W(K_L)$ of $K_L$ is investigated. The asymptotic order of the mean width difference $W(łK)-W((łK)_L)$ is maximized by the order obtained by polytopes and minimized by the order for smooth convex sets as $ł\to \infty$.
