论文标题
矫正概率和在单纯的顶点上达到最大值
Orthant probabilities and the attainment of maxima on a vertex of a simplex
论文作者
论文摘要
我们计算了与等效性的多元正态分布的矫正概率的界限，并使用这些界限以显示以下内容：对于$ k> 4 $，$ k $ - 均匀的多项式在$ n $变量中的可能性可在$ n $ n $ n $ dimementialsional simplex的顶点上获得最大值的相对最大值。我们为矫形概率获得的界限紧密至$ \ log（n）$因素。
We calculate bounds for orthant probabilities for the equicorrelated multivariate normal distribution and use these bounds to show the following: for degree $k>4$, the probability that a $k$-homogeneous polynomial in $n$ variables attains a relative maximum on a vertex of the $n$-dimensional simplex tends to one as the dimension $n$ grows. The bounds we obtain for the orthant probabilities are tight up to $\log(n)$ factors.
