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On the volume of the intersection of two $$L^ n_ p$$ balls. (English) Zbl 0704.60017
Note that for $$0<p<q<\infty$$ the $$L^ n_ p$$-ball $\{(t_ 1,...,t_ n)\in {\mathbb{R}}^ n:\;(1/n)\sum^{n}_{i=1}| t_ i|^ p\leq 1\}$ contains the $$L^ n_ q$$-ball. The authors prove that the volume left in the $$L^ n_ p$$-ball after removing a t-multiple of the $$L^ n_ q$$-ball is of order $$\exp (-ct^ pn^{p/q})$$. For this aim they exploit properties of i.i.d. random variables with density function $$(p/\Gamma (1/p))\exp (-t^ p)$$, $$t>0$$, which are related to $$L_ p$$ in the same way as Gaussian variables are related to $$L_ 2$$.
Reviewer: M.Zähle

##### MSC:
 6e+16 Inequalities; stochastic orderings
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