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

{"title":"和的指数周围的指数积的浓度","authors":"M. Anshelevich, Austin Pritchett","doi":"10.1080/00029890.2023.2185036","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Concentration of the Product of Exponentials Around the Exponential of the Sum\",\"authors\":\"M. Anshelevich, Austin Pritchett\",\"doi\":\"10.1080/00029890.2023.2185036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":7761,\"journal\":{\"name\":\"American Mathematical Monthly\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-03-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Mathematical Monthly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/00029890.2023.2185036\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2185036","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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

期刊介绍： The Monthly''s readers expect a high standard of exposition; they look for articles that inform, stimulate, challenge, enlighten, and even entertain. Monthly articles are meant to be read, enjoyed, and discussed, rather than just archived. Articles may be expositions of old or new results, historical or biographical essays, speculations or definitive treatments, broad developments, or explorations of a single application. Novelty and generality are far less important than clarity of exposition and broad appeal. Appropriate figures, diagrams, and photographs are encouraged. Notes are short, sharply focused, and possibly informal. They are often gems that provide a new proof of an old theorem, a novel presentation of a familiar theme, or a lively discussion of a single issue. Abstracts for articles or notes should entice the prospective reader into exploring the subject of the paper and should make it clear to the reader why this paper is interesting and important. The abstract should highlight the concepts of the paper rather than summarize the mechanics. The abstract is the first impression of the paper, not a technical summary of the paper. Excessive use of notation is discouraged as it can limit the interest of the broad readership of the MAA, and can limit search-ability of the article.