论文标题
高斯最低猜想的注释
A Note on the Gaussian Minimum Conjecture
论文作者
论文摘要
令$ n \ geq 2 $和$（x_i，1 \ leq i \ leq n）$为中心的高斯随机向量。高斯最低猜想说，$ e \ left（\ min_ {1 \ leq i \ leq n} | x_i | \ right）\ geq e \ left（\ min_ {1 \ leq i \ leq i \ leq i \ leq n} | y_i | \ y_i | \ right）$ y_1，y_1，\ y_1，\ ldots，y y_n $，y y_n $， $ e（x_i^2）= e（y_i^2）$ for任何$ i = 1，\ ldots，n $。在本说明中，我们将证明此猜想存在于且仅当$ n = 2 $时。
Let $n\geq 2$ and $(X_i,1\leq i\leq n)$ be a centered Gaussian random vector. The Gaussian minimum conjecture says that $E\left(\min_{1\leq i\leq n}|X_i|\right)\geq E\left(\min_{1\leq i\leq n}|Y_i|\right)$, where $Y_1,\ldots,Y_n$ are independent centered Gaussian random variables with $E(X_i^2)=E(Y_i^2)$ for any $i=1,\ldots,n$. In this note, we will show that this conjecture holds if and only if $n=2$.
