论文标题
UNINK定理用于对称准凸多项式
Unlinking Theorem for Symmetric Quasi-convex Polynomials
论文作者
论文摘要
让$μ_n$成为$ \ mathbb {r}^n $和$ x $的标准高斯度量，是$ \ mathbb {r}^n $的随机向量，与法律$μ_n$。 u-onjoxture指出，如果$ f $和$ g $是$ \ mathbb {r}^n $上的两个多项式，以至于$ f（x）$和$ g（x）$是独立的，那么存在正交转换$ l $ on $ on $ on $ \ mathbb {r} n $ and $ k $ $（x_1，\ cdots，x_k）$和$ g \ circ l $是$（x_ {k+1}，\ cdots，x_n）$的函数。在这种情况下，据说$ f $和$ g $是未链接的。在本说明中，我们证明，如果$ f（x）$和$ g（x）$是独立的，则将两个对称，准convex $ f $ $ f $和$ g $取消链接。
Let $μ_n$ be the standard Gaussian measure on $\mathbb{R}^n$ and $X$ be a random vector on $\mathbb{R}^n$ with the law $μ_n$. U-conjecture states that if $f$ and $g$ are two polynomials on $\mathbb{R}^n$ such that $f(X)$ and $g(X)$ are independent, then there exist an orthogonal transformation $L$ on $\mathbb{R}^n$ and an integer $k$ such that $f\circ L$ is a function of $(x_1,\cdots,x_k)$ and $g\circ L$ is a function of $(x_{k+1},\cdots,x_n)$. In this case, $f$ and $g$ are said to be unlinked. In this note, we prove that two symmetric, quasi-convex polynomials $f$ and $g$ are unlinked if $f(X)$ and $g(X)$ are independent.
