Toronto Probability

In this talk, we will discuss how a remarkable connection between operator theory and signal detection problems in random matrix theory leads to new insights regarding the detection of critical signals. These are signals that are right at the threshold of detectability using classical methods. We will begin by reviewing the basics of the signal detection problem in the simple case of the spiked GOE model. Then, we will explain the connection between the critical signal detection problem and spectral geometry/operator theory, and the new result that can be proved using this connection. Some of the results that will be discussed in this talk were obtained in collaboration with Promit Ghosal, Wilson Li, Yuchen Liao, and Mykhaylo Shkolnikov.