کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8898507 1631455 2018 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Gaussian polytopes: A cumulant-based approach
ترجمه فارسی عنوان
چندجمله گاوسی: رویکرد مبتنی بر انباشتگی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
The random convex hull of a Poisson point process in Rd whose intensity measure is a multiple of the standard Gaussian measure on Rd is investigated. The purpose of this paper is to invent a new viewpoint on these Gaussian polytopes that is based on cumulants and the general large deviation theory of Saulis and Statulevičius. This leads to new and powerful concentration inequalities, moment bounds, Marcinkiewicz-Zygmund-type strong laws of large numbers, central limit theorems and moderate deviation principles for the volume and the face numbers. Corresponding results are also derived for the empirical measures induced by these key geometric functionals, taking thereby care of their spatial profiles.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 47, August 2018, Pages 1-41
نویسندگان
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