零温度极限下分离构型中ABC模型的演化

IF 1.2 2区数学 Q2 STATISTICS & PROBABILITY

Annales De L Institut Henri Poincare-probabilites Et Statistiques Pub Date : 2014-03-19 DOI:10.1214/14-AIHP648

R. Misturini

{"title":"零温度极限下分离构型中ABC模型的演化","authors":"R. Misturini","doi":"10.1214/14-AIHP648","DOIUrl":null,"url":null,"abstract":"We consider the ABC model on a ring in a strongly asymmetric regime. The main result asserts that the particles almost always form three pure domains (one of each species) and that this segregated shape evolves, in a proper time scale, as a Brownian motion on the circle, which may have a drift. This is, to our knowledge, the first proof of a zero-temperature limit for a non-reversible dynamics whose invariant measure is not explicitly known.","PeriodicalId":7902,"journal":{"name":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","volume":"127 1","pages":"669-702"},"PeriodicalIF":1.2000,"publicationDate":"2014-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Evolution of the ABC model among the segregated configurations in the zero-temperature limit\",\"authors\":\"R. Misturini\",\"doi\":\"10.1214/14-AIHP648\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the ABC model on a ring in a strongly asymmetric regime. The main result asserts that the particles almost always form three pure domains (one of each species) and that this segregated shape evolves, in a proper time scale, as a Brownian motion on the circle, which may have a drift. This is, to our knowledge, the first proof of a zero-temperature limit for a non-reversible dynamics whose invariant measure is not explicitly known.\",\"PeriodicalId\":7902,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-probabilites Et Statistiques\",\"volume\":\"127 1\",\"pages\":\"669-702\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2014-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-probabilites Et Statistiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/14-AIHP648\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-probabilites Et Statistiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/14-AIHP648","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 10

摘要

我们考虑了环在强不对称状态下的ABC模型。主要结果断言，粒子几乎总是形成三个纯域(每种一个)，并且这种分离的形状在适当的时间尺度上演变为圆周上的布朗运动，可能有漂移。据我们所知，这是对不可逆动力学的零温度极限的第一个证明，它的不变测度是未知的。

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

Evolution of the ABC model among the segregated configurations in the zero-temperature limit

We consider the ABC model on a ring in a strongly asymmetric regime. The main result asserts that the particles almost always form three pure domains (one of each species) and that this segregated shape evolves, in a proper time scale, as a Brownian motion on the circle, which may have a drift. This is, to our knowledge, the first proof of a zero-temperature limit for a non-reversible dynamics whose invariant measure is not explicitly known.

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

Annales De L Institut Henri Poincare-probabilites Et Statistiques 数学-统计学与概率论

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Probability and Statistics section of the Annales de l’Institut Henri Poincaré is an international journal which publishes high quality research papers. The journal deals with all aspects of modern probability theory and mathematical statistics, as well as with their applications.