Horng‐Tzer Yau

Universality for the global spectrum of random inner-product kernel matrices in the polynomial regime

We consider certain large random matrices, called random inner-product kernel matrices, which are essentially given by a nonlinear function f applied entrywise to a sample-covariance matrix, f(XTX), where X∈Rd×N is random and normalized in such a way that f typically has order-on...

Edge universality of random regular graphs of growing degrees

We consider the statistics of extreme eigenvalues of random d-regular graphs, with Nc≤d≤N1/3−c for arbitrarily small c>0. We prove that in this regime, the fluctuations of extreme eigenvalues are given by the Tracy–Widom distribution. As a consequence, about 69% of d-regular grap...