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
\(4/\beta\).
An isolated quantum many-body system may be a reservoir that
thermalizes its constituents. I will explore an example of the
interplay of this thermalization and spontaneous symmetry-breaking,
in the ferromagnetic phase of an infinite-range quantum...
