论文标题
泊松近似值和威布尔渐近学在数字的几何形状中
Poisson approximation and Weibull asymptotics in the geometry of numbers
论文作者
论文摘要
Minkowski的第一个定理和Dirichlet的近似定理在欧几里得空间域中包含的晶格点上的某些最小值上提供了上限。我们研究了这种最小值的分布，并在某些技术条件下表明，它们在$ \ br^d $中的非晶体晶格空间上表现出了微生渐近性。这是由非常通用的泊松近似结果缩小了应该具有独立感兴趣的目标的结果。此外，我们在附录中表明，可以从我们的分布结果中推断出Kleinbock-Margulis，Khinchin和Gallagher的对数定律。
Minkowski's First Theorem and Dirichlet's Approximation Theorem provide upper bounds on certain minima taken over lattice points contained in domains of Euclidean spaces. We study the distribution of such minima and show, under some technical conditions, that they exhibit Weibull asymptotics with respect to different natural measures on the space of unimodular lattices in $\bR^d$. This follows from very general Poisson approximation results for shrinking targets which should be of independent interest. Furthermore, we show in the appendix that the logarithm laws of Kleinbock-Margulis, Khinchin and Gallagher can be deduced from our distributional results.
