Previous Special Year Seminar

We consider a system of harmonic oscillators with stochastic perturbations of the dynamics that conserve energy and momentum. In the one dimensional unpinned case, under proper space-time rescaling, Wigner distribution of energy converges to the...

Based on joint work with A. Guionnet (MIT). The beta ensemble is a particular model consisting of N strongly correlated real random variables. For specific values of beta, it is be realized by the eigenvalues of a random hermitian matrix whose...

In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly-oriented copies of a molecule. The cryo-EM problem is to use the resulting set of noisy 2D projection images taken at unknown directions to reconstruct...

The study of the Gaussian limit of linear statistics of eigenvalues of random matrices and related processes, like determinantal processes, has been an important theme in random matrix theory. I will review some results starting with the strong...

What is the volume of the set of singular symmetric matrices of norm one? What is the probability that a random plane misses this set? What is the expected "topology" of the intersection of random quadric hypersurfaces? In this talk I will combine...

I discuss a renormalization group method to derive diffusion from time reversible quantum or classical microscopic dynamics. I start with the problem of return to equilibrium and derivation of Brownian motion for a quantum particle interacting with...

The quantum random energy model is a random matrix of Schroedinger type: a Laplacian on the hypercube plus a random potential. It features in various contexts from mathematical biology to quantum information theory as well as an effective...

We develop spectral theory for the generator of the \(q\)-Boson particle system. Our central result is a Plancherel type isomorphism theorem for this system; it implies completeness of the Bethe ansatz in infinite volume and enables us to solve...

In the early 1960's Dyson and Mehta found that the CSE relates to the COE. I'll discuss generalizations as well as other settings in random matrix theory in which \(\beta\) relates to \(4/\beta\).