{"title":"A note on the capacity estimate in metastability for generic configurations","authors":"Benny Avelin, Vesa Julin","doi":"10.1007/s00229-024-01555-1","DOIUrl":null,"url":null,"abstract":"<p>In this paper we further develop the ideas from Geometric Function Theory initially introduced in Avelin et al. (Commun Math Phys 404:401–437, 2023), to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First, the graph theoretical connection enables us to exactly compute the pre-factor in the capacity. Second, we complete the method from Avelin et al. (Commun Math Phys 404:401–437, 2023) by providing an upper bound using Geometric Function Theory together with Thompson’s principle, avoiding explicit constructions of test functions.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01555-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we further develop the ideas from Geometric Function Theory initially introduced in Avelin et al. (Commun Math Phys 404:401–437, 2023), to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First, the graph theoretical connection enables us to exactly compute the pre-factor in the capacity. Second, we complete the method from Avelin et al. (Commun Math Phys 404:401–437, 2023) by providing an upper bound using Geometric Function Theory together with Thompson’s principle, avoiding explicit constructions of test functions.
在本文中,我们进一步发展了最初在阿维林等人(Commun Math Phys 404:401-437, 2023)一文中提出的几何函数论的思想,推导出了任意配置的可转移性容量估计。本文的新颖之处有两方面。首先,图论联系使我们能够精确计算容量中的预因子。其次,我们利用几何函数理论和汤普森原理提供了一个上界,避免了测试函数的明确构造,从而完善了阿维林等人(Commun Math Phys 404:401-437, 2023)的方法。