NSF/CBMS Regional Conference in the Mathematical Sciences-"Probabilistic and Combinatorial Approach in Analysis"

在不同时期，概率和组合技术在泛函和调和分析方面取得了重要进展。在许多情况下，明确的结构已被证明是难以捉摸的，但有可能表明，当某些参数随机变化时，现象发生的概率很高。在其他时候，当明确的结构已经超出了范围，组合技术已被有效地应用，以提供存在证明。近年来，这两种方法在凸几何、几何泛函分析和大矩阵理论以及信号处理和学习理论中得到了广泛的应用。相反，概率论中的几个重要问题，特别是随机过程理论中的一些问题，已经用几何泛函分析的方法解决了。在肯特州立大学组织一次关于功能分析中的概率和组合方法的有影响力的CBMS会议的机会之窗已经打开。Mark Rudelson教授是该学科的主要专家之一，他同意担任会议的首席讲师。

At various times, probabilistic and combinatorial techniques have led to important advances in functional and harmonic analysis. In many situations, explicit constructions have proved elusive, but it has been possible to show that phenomena occur with high probability when certain parameters are varied randomly. At othertimes when explicit constructions have been beyond reach, combinatorial techniques have been applied effectively to provide existence proofs. Recently, these two types of approach have been used together to great effect in establishing new results in convex geometry, geometrical functional analysis and the theory oflarge matrices, as well as in signal processing and learning theory. Conversely, several important problems in probability, especially in the theory of random processes, have been solved using methods of geometric functional analysis. A window of opportunity has opened for the organization of an influential CBMS conference on probabilistic and combinatorial methods in functional analysis at Kent State University. Professor Mark Rudelson, one of the leading experts in the subject, has agreed to serve as the Principal Lecturer of the conference.