Around two theorems and a lemma by Lucio Russo

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2018-05-29 DOI:10.2140/MEMOCS.2018.6.69

I. Benjamini, G. Kalai

引用次数: 2

Abstract

We did not meet Lucio Russo in person but his mathematical work greatly influenced our own and his wide horizons and interests in physics, mathematics, philosophy, and history greatly inspired us. We describe here two directions of study following early work of Russo. The first section follow the famous Russo-Seymour-Welsh theorem regarding critical planar percolation. The second section follows the basic ”Russo’s lemma” and deep ”Russo’s 0-1 law”. In each direction we present one central conjecture.

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围绕卢西奥·鲁索的两个定理和一个引理

我们没有见过卢西奥·鲁索本人，但他的数学工作对我们影响很大，他在物理、数学、哲学和历史方面的广阔视野和兴趣极大地激励了我们。我们在这里描述了罗素早期工作之后的两个研究方向。第一部分遵循著名的关于临界平面渗流的Russo-Seymour-Welsh定理。第二部分遵循基本的“Russo引理”和深层的“Russo 0-1定律”。在每个方向上，我们都提出一个中心猜想。

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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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.