افاق للعلوم
Volume 5, Numéro 1, Pages 407-417
2020-01-02

Diameter Of Convex Sets (bodies) & Concentration Of Measure



Authors : عطية خالد .

Abstract

Abstract: Under the notion of concentration of measure and (LDP) we found that the diameter of a section of any convex bodies will depends basically in the isotropic constant L_K of the polar body of the convex body and we found that diam(K∩E)≤C√p diam(K∩K^0) where E⊂K^0. المستخلص: تحت مفهوم تركيز الحجم و مبدأ الانحراف الأعظم وجدنا أن قطر القطاع لأي جسم محدب يعتمد بصورة أساسية على ثابت التحدب L_K للجسم القطبي لأي جسم محدب. و وجدنا أنه diam(K∩E)≤C√p diam(K∩K^0 ) حيث E⊂K^0 .

Keywords

Key words: Embedding, Concentration of Measure, Large Deviation Principle, Polar Body.

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