关于树栖气体与特定参数的负相关关系

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2024-06-04 DOI:10.1016/j.spl.2024.110174

Xiangyu Huang

{"title":"关于树栖气体与特定参数的负相关关系","authors":"Xiangyu Huang","doi":"10.1016/j.spl.2024.110174","DOIUrl":null,"url":null,"abstract":"<div>Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter <math><mrow><mi>β</mi><mo>></mo><mn>0</mn></mrow></math> per edge. This model can be considered as the limit of the <math><mi>q</mi></math>-states random cluster model with <math><mrow><mi>p</mi><mo>=</mo><mi>β</mi><mi>q</mi></mrow></math> as <math><mrow><mi>q</mi><mo>→</mo><mn>0</mn></mrow></math>. A natural question arises regarding the existence and performance of the weak limit of Arboreal Gas as the graph size goes to infinity. The answer to this question relies on the negative correlation of Arboreal Gas, which is still an open problem. This paper primarily focuses on the negative correlation of Arboreal Gas and provides some results for specific parameters.</div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"213 ","pages":"Article 110174"},"PeriodicalIF":0.9000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On negative correlation of Arboreal Gas for specific parameters\",\"authors\":\"Xiangyu Huang\",\"doi\":\"10.1016/j.spl.2024.110174\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter <math><mrow><mi>β</mi><mo>></mo><mn>0</mn></mrow></math> per edge. This model can be considered as the limit of the <math><mi>q</mi></math>-states random cluster model with <math><mrow><mi>p</mi><mo>=</mo><mi>β</mi><mi>q</mi></mrow></math> as <math><mrow><mi>q</mi><mo>→</mo><mn>0</mn></mrow></math>. A natural question arises regarding the existence and performance of the weak limit of Arboreal Gas as the graph size goes to infinity. The answer to this question relies on the negative correlation of Arboreal Gas, which is still an open problem. This paper primarily focuses on the negative correlation of Arboreal Gas and provides some results for specific parameters.</div>\",\"PeriodicalId\":49475,\"journal\":{\"name\":\"Statistics & Probability Letters\",\"volume\":\"213 \",\"pages\":\"Article 110174\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics & Probability Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167715224001433\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224001433","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

Arboreal Gas 是一种图上的（无根）随机森林，其概率由每条边的参数 β>0 决定。该模型可视为 q→0 时 p=βq 的 q 态随机簇模型的极限。当图的大小达到无穷大时，自然会产生一个关于 Arboreal Gas 弱极限的存在和性能的问题。这个问题的答案取决于 Arboreal Gas 的负相关，而这仍是一个未决问题。本文主要关注 Arboreal Gas 的负相关性，并提供了一些特定参数的结果。

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

On negative correlation of Arboreal Gas for specific parameters

Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter $β > 0$ per edge. This model can be considered as the limit of the $q$ -states random cluster model with $p = β q$ as $q \to 0$ . A natural question arises regarding the existence and performance of the weak limit of Arboreal Gas as the graph size goes to infinity. The answer to this question relies on the negative correlation of Arboreal Gas, which is still an open problem. This paper primarily focuses on the negative correlation of Arboreal Gas and provides some results for specific parameters.

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

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.