December 13 to December 17, 2010
American Institute of Mathematics,
Palo Alto, California
Terence Tao and Van Vu
This workshop will focus on recent developments on limiting distributions
concerning spectrum of a random matrix. We will focus on the two main
types of limiting distributions:
Both global and local laws are well understood in few special cases
(such as GUE). The general belief is that these laws should hold for
much larger classes of random matrices. This is known as the
universality phenomenon (or invariance principle). This phenomenon
has been supported by overwhelming numerical data and various
conjectures, many of which
(such as the Circular Law conjecture and Mehta conjectures) are among
the most well known problems in the field.
- Global: One would like to understand the limiting law of the
generated by all eigenvalues. The most famous example here is the
semi-circle law regarding the eigenvalues of random Hermitian
matrices, discovered by Wigner in the 1950's.
- Local: One would like to understand the limiting law of
fluctuation of individual
eigenvalues (say the largest or smallest eigenvalues, or in general,
the kth eigenvalues for any k), or local interaction among
eigenvalues in a small neighborhood. Typical examples here are the
Tracy-Widom law (for the extremal eigenvalues) and Dyson laws (for the
distribution of gaps between consecutive eigenvalues and for
In this workshop, we aim to first provide an overview about recent
developments that establish
(both global and local) universality in many important cases and in addition, we
would like to discuss the techniques and directions for future
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.
A list of open problems.