A note on the capacity estimate in metastability for generic configurations

Pub Date : 2024-04-08 DOI:10.1007/s00229-024-01555-1
Benny Avelin, Vesa Julin
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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.

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关于一般配置的代谢能力估计的说明
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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