Student Analysis Seminar

The study of spiked sample covariance matrices where the covariance matrices take the form of an identity matrix plus a low rank perturbation plays an important role in high dimensional statistics. In the talk I will explain the well-known phase transition due to Baik-Ben Arous-Peche on the limiting behaviors of the largest eigenvalue of the spiked Wishart matrices and its interpretation in terms of signal detection. On the other hand there is a remarkable equality in distribution between the largest eigenvalue of (spiked) complex Wishart matrices and the last passage time in (inhomogeneous) exponential last passage percolation model (or equivalently totally asymmetric simple exclusion process with particle and site dependent jumping rates). I will also explain how one understands the BBP transition in these contexts. Time permitting I will discuss my ongoing work on the extensions to multi-time joint distributions. Speaker(s): Yuchen Liao (University of Michigan)