某些平面准晶体方向间大间隙的渐近估计

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-05-30 DOI:10.1112/jlms.70187

Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu

{"title":"某些平面准晶体方向间大间隙的渐近估计","authors":"Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu","doi":"10.1112/jlms.70187","DOIUrl":null,"url":null,"abstract":"For quasicrystals of cut-and-project type in <math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mi>d</mi>\n </msup>\n <annotation>$\\mathbb {R}^d$</annotation>\n </semantics></math>, it was proved by Marklof and Strömbergsson [Int. Math. Res. Not. IMRN (2015), no. 15, 6588–6617; erratum, ibid. 2020] that the limit local statistical properties of the directions to the points in the set are described by certain <math>\n <semantics>\n <mrow>\n <msub>\n <mo>SL</mo>\n <mi>d</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>R</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\operatorname{SL}_d(\\mathbb {R})$</annotation>\n </semantics></math>-invariant point processes. In this paper, we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70187","citationCount":"0","resultStr":"{\"title\":\"Asymptotic estimates of large gaps between directions in certain planar quasicrystals\",\"authors\":\"Gustav Hammarhjelm, Andreas Strömbergsson, Shucheng Yu\",\"doi\":\"10.1112/jlms.70187\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For quasicrystals of cut-and-project type in <math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mi>d</mi>\\n </msup>\\n <annotation>$\\\\mathbb {R}^d$</annotation>\\n </semantics></math>, it was proved by Marklof and Strömbergsson [Int. Math. Res. Not. IMRN (2015), no. 15, 6588–6617; erratum, ibid. 2020] that the limit local statistical properties of the directions to the points in the set are described by certain <math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mo>SL</mo>\\n <mi>d</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>R</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\operatorname{SL}_d(\\\\mathbb {R})$</annotation>\\n </semantics></math>-invariant point processes. In this paper, we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals.\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"111 6\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-05-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70187\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70187\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70187","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于R d$ \mathbb {R}^d$中的切割投影型准晶体，由Marklof和Strömbergsson [Int]证明。数学。研究》。IMRN (2015), no。15, 6588 - 6617;[[erratum, ibid. 2020]]证明了集合中点的方向的极限局部统计性质是由某些SL d(R)$ \operatorname{SL}_d(\mathbb {R})$ -不变点过程描述的。在本文中，我们详细地研究了某些特定类平面准晶体方向上的极限间隙统计量的尾部渐近性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Asymptotic estimates of large gaps between directions in certain planar quasicrystals

查看原文本刊更多论文

Asymptotic estimates of large gaps between directions in certain planar quasicrystals

For quasicrystals of cut-and-project type in $R^{d}$ , it was proved by Marklof and Strömbergsson [Int. Math. Res. Not. IMRN (2015), no. 15, 6588–6617; erratum, ibid. 2020] that the limit local statistical properties of the directions to the points in the set are described by certain ${SL}_{d} (R)$ -invariant point processes. In this paper, we make a detailed study of the tail asymptotics of the limiting gap statistics of the directions, for certain specific classes of planar quasicrystals.

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.