تقرير
A phase transition for the probability of being a maximum among random vectors with general iid coordinates
| العنوان: | A phase transition for the probability of being a maximum among random vectors with general iid coordinates |
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| المؤلفون: | Jacobovic, Royi, Zuk, Or |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Statistics Theory, 60C05, 60F20, 62E20 |
| الوصف: | Consider $n$ iid real-valued random vectors of size $k$ having iid coordinates with a general distribution function $F$. A vector is a maximum if and only if there is no other vector in the sample which weakly dominates it in all coordinates. Let $p_{k,n}$ be the probability that the first vector is a maximum. The main result of the present paper is that if $k\equiv k_n$ is growing at a slower (faster) rate than a certain factor of $\log(n)$, then $p_{k,n} \rightarrow 0$ (resp. $p_{k,n}\rightarrow1$) as $n\to\infty$. Furthermore, the factor is fully characterized as a functional of $F$. We also study the effect of $F$ on $p_{k,n}$, showing that while $p_{k,n}$ may be highly affected by the choice of $F$, the phase transition is the same for all distribution functions up to a constant factor. Comment: 17 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2112.15534 |
| رقم الأكسشن: | edsarx.2112.15534 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |