| 关于对称拟凸多项式的不相连定理 |
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| 引用本文： | 洪和静,胡泽春. 关于对称拟凸多项式的不相连定理[J]. 应用概率统计, 2022, 0(1): 151-158 |
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| 作者姓名： | 洪和静 胡泽春 |
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| 作者单位： | 南京大学数学系;南京方腾医药技术有限公司;四川大学数学学院 |
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| 基金项目： | The project was supported by the National Natural Science Foundation of China(Grant Nos.12171335,11871184). |
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| 摘 要： | 假定μn为Rn上的标准高斯测度,X为Rn上的随机向量,分布为μn.不相连猜测说的是:如果f与g为Rn上的两个多项式,而且f(X)与g(X)相互独立,则存在Rn上的正交变换Y = LX及整数k使得f o L-1为(y1,y2,…,yk)的函数,goL-1为(yk+1,yk+2,…,yn)的函数.此时,称f与g不相连.在这...
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| 关 键 词： | 不相连猜测 拟凸多项式 高斯相关猜测 |
Unlinking Theorem for Symmetric Quasi-Convex Polynomials |
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| HONG Hejing,HU Zechun. Unlinking Theorem for Symmetric Quasi-Convex Polynomials[J]. Chinese Journal of Applied Probability and Statisties, 2022, 0(1): 151-158 |
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| Authors: | HONG Hejing HU Zechun |
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| Affiliation: | (Department of Mathematics,Nanjing University,Nanjing,210093,China;Clinchoice Inc.of Nanjing,Nanjing,211100,China;College of Mathematics,Sichuan University,Chengdu,610065,China) |
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| Abstract: | Letμn be the standard Gaussian measure on Rnand X be a random vector on Rnwith the lawμn.U-conjecture states that if f and g are two polynomials on Rnsuch that f(X)and g(X)are independent,then there exist an orthogonal transformation Y=LX on Rnand an integer k such that f?L-1is a function of(yi,y2,…,yk)and g?L-1is a function of(yk+1,yk+2,…,yn).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. |
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| Keywords: | U-conjecture quasi-convex polynomial Gaussian correlation conjecture |
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