标题： 强收敛现象 显示英文标题

标题： The strong convergence phenomenon

摘要： 在一篇具有开创性的2005年论文中，Haagerup和Thorbj{\o }rnsen发现，任何独立复高斯随机矩阵的非交换多项式的范数都会收敛到由Voiculescu自由概率论产生的极限算子族的范数。 近年来，新的方法使得在更广泛的情况下建立这种强收敛性质成为可能，并且可以获得更强的定量形式的强收敛现象。 这些方法反过来导致了许多在随机图、双曲曲面和算子代数领域长期悬而未决的问题的显著应用，并提供了灵活的新工具，使随机矩阵的研究得以在出人意料的广度上进行。 本综述旨在介绍这一系列思想。 显示英文摘要

摘要： In a seminal 2005 paper, Haagerup and Thorbj{\o}rnsen discovered that the norm of any noncommutative polynomial of independent complex Gaussian random matrices converges to that of a limiting family of operators that arises from Voiculescu's free probability theory. In recent years, new methods have made it possible to establish such strong convergence properties in much more general situations, and to obtain even more powerful quantitative forms of the strong convergence phenomenon. These, in turn, have led to a number of spectacular applications to long-standing open problems on random graphs, hyperbolic surfaces, and operator algebras, and have provided flexible new tools that enable the study of random matrices in unexpected generality. This survey aims to provide an introduction to this circle of ideas.