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 other times 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 of large 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.
