和的指数周围的指数积的浓度

IF 0.4 4区数学 Q4 MATHEMATICS American Mathematical Monthly Pub Date : 2023-03-17 DOI:10.1080/00029890.2023.2185036

M. Anshelevich, Austin Pritchett

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引用次数: 0

摘要

摘要对于两个矩阵A和B，且n大，我们证明了n个因子的乘积与n个因子的乘积大多数接近。这扩展了Lie-Trotter公式。初等证明是基于词与格路径之间的关系、二项式系数的渐近性和矩阵不等式。该结果适用于两个以上的矩阵。

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The Concentration of the Product of Exponentials Around the Exponential of the Sum

Abstract For two matrices A and B, and large n, we show that most products of n factors of and n factors of are close to . This extends the Lie-Trotter formula. The elementary proof is based on the relation between words and lattice paths, asymptotics of binomial coefficients, and matrix inequalities. The result holds for more than two matrices.

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来源期刊

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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