随机电导模型研究进展

IF 1.3 Q2 STATISTICS & PROBABILITY

Probability Surveys Pub Date : 2011-12-01 DOI:10.1214/11-PS190

M. Biskup

{"title":"随机电导模型研究进展","authors":"M. Biskup","doi":"10.1214/11-PS190","DOIUrl":null,"url":null,"abstract":"Recent progress on the understanding of the Random Conductance Model is \nreviewed and commented. A particular emphasis is on the results on the \nscaling limit of the random walk among random conductances for almost \nevery realization of the environment, observations on the behavior of \nthe effective resistance as well as the scaling limit of certain models \nof gradient fields with non-convex interactions. The text is an \nexpanded version of the lecture notes for a course delivered at the \n2011 Cornell Summer School on Probability.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":"8 1","pages":"294-373"},"PeriodicalIF":1.3000,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1214/11-PS190","citationCount":"202","resultStr":"{\"title\":\"Recent progress on the Random Conductance Model\",\"authors\":\"M. Biskup\",\"doi\":\"10.1214/11-PS190\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent progress on the understanding of the Random Conductance Model is \\nreviewed and commented. A particular emphasis is on the results on the \\nscaling limit of the random walk among random conductances for almost \\nevery realization of the environment, observations on the behavior of \\nthe effective resistance as well as the scaling limit of certain models \\nof gradient fields with non-convex interactions. The text is an \\nexpanded version of the lecture notes for a course delivered at the \\n2011 Cornell Summer School on Probability.\",\"PeriodicalId\":46216,\"journal\":{\"name\":\"Probability Surveys\",\"volume\":\"8 1\",\"pages\":\"294-373\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2011-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1214/11-PS190\",\"citationCount\":\"202\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Surveys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/11-PS190\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Surveys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/11-PS190","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 202

摘要

综述了随机电导模型的最新研究进展。特别强调的是对几乎每一个环境实现的随机电导间随机游走的标度极限的结果，对有效电阻行为的观察以及具有非凸相互作用的梯度场的某些模型的标度极限。本文是2011年康奈尔大学概率暑期学校课堂讲稿的扩充版。

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

Recent progress on the Random Conductance Model

Recent progress on the understanding of the Random Conductance Model is reviewed and commented. A particular emphasis is on the results on the scaling limit of the random walk among random conductances for almost every realization of the environment, observations on the behavior of the effective resistance as well as the scaling limit of certain models of gradient fields with non-convex interactions. The text is an expanded version of the lecture notes for a course delivered at the 2011 Cornell Summer School on Probability.

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

Probability Surveys STATISTICS & PROBABILITY-

CiteScore

4.70

自引率

0.00%

发文量