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
\(4/\beta\).
