量子布尔立方体的几何影响

arXiv - MATH - Functional Analysis Pub Date : 2024-08-30 DOI:arxiv-2409.00224

David P. Blecher, Li Gao, Bang Xu

{"title":"量子布尔立方体的几何影响","authors":"David P. Blecher, Li Gao, Bang Xu","doi":"arxiv-2409.00224","DOIUrl":null,"url":null,"abstract":"In this work, we study three problems related to the $L_1$-influence on\nquantum Boolean cubes. In the first place, we obtain a dimension free bound for\n$L_1$-influence, which implies the quantum $L^1$-KKL Theorem result obtained by\nRouze, Wirth and Zhang. Beyond that, we also obtain a high order quantum\nTalagrand inequality and quantum $L^1$-KKL theorem. Lastly, we prove a\nquantitative relation between the noise stability and $L^1$-influence. To this\nend, our technique involves the random restrictions method as well as semigroup\ntheory.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometric influences on quantum Boolean cubes\",\"authors\":\"David P. Blecher, Li Gao, Bang Xu\",\"doi\":\"arxiv-2409.00224\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we study three problems related to the $L_1$-influence on\\nquantum Boolean cubes. In the first place, we obtain a dimension free bound for\\n$L_1$-influence, which implies the quantum $L^1$-KKL Theorem result obtained by\\nRouze, Wirth and Zhang. Beyond that, we also obtain a high order quantum\\nTalagrand inequality and quantum $L^1$-KKL theorem. Lastly, we prove a\\nquantitative relation between the noise stability and $L^1$-influence. To this\\nend, our technique involves the random restrictions method as well as semigroup\\ntheory.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.00224\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.00224","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在这项工作中，我们研究了与量子布尔立方体上的 $L_1$ 影响有关的三个问题。首先，我们得到了$L_1$-影响的无维约束，这意味着鲁兹、维斯和张得到的量子$L^1$-KKL定理结果。除此之外，我们还得到了高阶量子塔拉格兰德不等式和量子 $L^1$-KKL 定理。最后，我们证明了噪声稳定性与 $L^1$ 影响之间的定量关系。为此，我们的技术涉及随机限制方法和半规则理论。

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

Geometric influences on quantum Boolean cubes

In this work, we study three problems related to the $L_1$-influence on quantum Boolean cubes. In the first place, we obtain a dimension free bound for $L_1$-influence, which implies the quantum $L^1$-KKL Theorem result obtained by Rouze, Wirth and Zhang. Beyond that, we also obtain a high order quantum Talagrand inequality and quantum $L^1$-KKL theorem. Lastly, we prove a quantitative relation between the noise stability and $L^1$-influence. To this end, our technique involves the random restrictions method as well as semigroup theory.

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

arXiv - MATH - Functional Analysis

自引率

0.00%

发文量