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

在不同的时期，概率和组合技术导致了泛函和调和分析的重要进展。在许多情况下，显式结构已被证明是难以捉摸的，但已经有可能表明，当某些参数随机变化时，现象发生的概率很高。在其他时候，当显式结构已经遥不可及时，组合技术已经被有效地应用来提供存在的证据。近年来，这两种方法的结合在凸几何、几何泛函分析和大矩阵理论以及信号处理和学习理论方面都取得了很大的效果。相反，概率中的几个重要问题，特别是随机过程理论中的一些重要问题，已经用几何泛函分析的方法解决了。在肯特州立大学组织了一次有影响力的关于函数分析中的概率和组合方法的建立信任措施会议的机会之窗已经打开。该课题的主要专家之一Mark Rudelson教授已同意担任是次会议的首席讲师。

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.