Reversible Poisson-Kirchhoff Systems

IF 0.5 4区 数学 Q3 MATHEMATICS
Alexandre Boyer, Jérôme Casse, Nathanaël Enriquez, Arvind Singh
{"title":"Reversible Poisson-Kirchhoff Systems","authors":"Alexandre Boyer, Jérôme Casse, Nathanaël Enriquez, Arvind Singh","doi":"10.24033/bsmf.2863","DOIUrl":null,"url":null,"abstract":"We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model. This class of systems generalizes several classical processes of the same kind, such as Hammersley's broken line processes involved in Last Passage Percolation theory or such as the six-vertex model for some special sets of parameters. The novelty comes here from the introduction of a weight associated with each line. The lines are initially generated by spatially homogeneous weighted Poisson Point Process and their evolution (turn, split, crossing) are ruled by a Markovian dynamics which preserves Kirchhoff's node law for the line weights at each intersection. Among others, we derive some new explicit invariant measures for some bullet models as well as new reversible properties for some six-vertex models with an external electromagnetic field.","PeriodicalId":55332,"journal":{"name":"Bulletin De La Societe Mathematique De France","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin De La Societe Mathematique De France","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24033/bsmf.2863","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model. This class of systems generalizes several classical processes of the same kind, such as Hammersley's broken line processes involved in Last Passage Percolation theory or such as the six-vertex model for some special sets of parameters. The novelty comes here from the introduction of a weight associated with each line. The lines are initially generated by spatially homogeneous weighted Poisson Point Process and their evolution (turn, split, crossing) are ruled by a Markovian dynamics which preserves Kirchhoff's node law for the line weights at each intersection. Among others, we derive some new explicit invariant measures for some bullet models as well as new reversible properties for some six-vertex models with an external electromagnetic field.
可逆泊松-基尔霍夫系统
我们在四分之一平面上定义了一类一般的水平和垂直加权折线随机系统,并证明了它们的分布是平移不变的。这种不变性源于模型的可逆性。这类系统概括了几种经典的同类型过程,如最后通道渗流理论中涉及的Hammersley折线过程或某些特殊参数集的六顶点模型。这里的新奇之处在于引入了与每条线相关联的权重。这些线最初是由空间均匀加权泊松点过程生成的,它们的演变(转弯、分裂、交叉)由马尔可夫动力学控制,该动力学保留了每个交点线权的基尔霍夫节点定律。在此基础上,我们推导了一些弹丸模型的新的显式不变测度,以及一些具有外电磁场的六顶点模型的新的可逆性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
0.90
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: The Bulletin de la Société Mathématique de France was founded in 1873, and it has published works by some of the most prestigious mathematicians, including for example H. Poincaré, E. Borel, E. Cartan, A. Grothendieck and J. Leray. It continues to be a journal of the highest mathematical quality, using a rigorous refereeing process, as well as a discerning selection procedure. Its editorial board members have diverse specializations in mathematics, ensuring that articles in all areas of mathematics are considered. Promising work by young authors is encouraged.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信