随机映射中模式出现的渐近正态性

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-04-11 DOI:10.1112/jlms.70149

Michael Drmota, Eva-Maria Hainzl, Nick Wormald

{"title":"随机映射中模式出现的渐近正态性","authors":"Michael Drmota, Eva-Maria Hainzl, Nick Wormald","doi":"10.1112/jlms.70149","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to study the limiting distribution of special additive functionals on random planar maps, namely the number of occurrences of a given pattern. The main result is a central limit theorem for these pattern counts in the case of patterns with a simple boundary. The proof relies on a combination of analytic and combinatorial methods together with a moment method due to Gao and Wormald [Probab. Theory Relat. Fields 130 (2004), 368–376]. It is an important issue to handle the overlap structure of two patterns which is the main difficulty in the proof.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic normality of pattern occurrences in random maps\",\"authors\":\"Michael Drmota, Eva-Maria Hainzl, Nick Wormald\",\"doi\":\"10.1112/jlms.70149\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to study the limiting distribution of special additive functionals on random planar maps, namely the number of occurrences of a given pattern. The main result is a central limit theorem for these pattern counts in the case of patterns with a simple boundary. The proof relies on a combination of analytic and combinatorial methods together with a moment method due to Gao and Wormald [Probab. Theory Relat. Fields 130 (2004), 368–376]. It is an important issue to handle the overlap structure of two patterns which is the main difficulty in the proof.\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"111 4\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-04-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.70149\",\"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://onlinelibrary.wiley.com/doi/10.1112/jlms.70149","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

本文的目的是研究特殊加性泛函在随机平面映射上的极限分布，即给定图形出现的次数。主要结果是在具有简单边界的模式的情况下，这些模式计数的中心极限定理。该证明依赖于解析和组合方法的结合以及Gao和Wormald [Probab]的矩量法。代数理论。环境科学学报（2004），368-376。如何处理两种模式的重叠结构是证明中的一个重要问题，也是证明的主要难点。

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

Asymptotic normality of pattern occurrences in random maps

The purpose of this paper is to study the limiting distribution of special additive functionals on random planar maps, namely the number of occurrences of a given pattern. The main result is a central limit theorem for these pattern counts in the case of patterns with a simple boundary. The proof relies on a combination of analytic and combinatorial methods together with a moment method due to Gao and Wormald [Probab. Theory Relat. Fields 130 (2004), 368–376]. It is an important issue to handle the overlap structure of two patterns which is the main difficulty in the proof.

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.