In the time-dependent density functional theory framework, the optical absorption spectrum of a molecular system can be estimated from the trace of the dynamic polarizability associated with the linear response of the charge density to an external potential perturbation of the ground state Hamiltonian. Although an accurate description of the abs...

Creator:

Yang, Chao (Lawrence Berkeley National Laboratory)

Created:

2017-04-25

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The prototypical joint density of eigenvalues of a random matrix contains as a factor a power of the absolute value of the Vandermonde determinant in the variables of integration. The most nuanced statistical information can be derived when this power, denoted beta, takes the value 1, 2 or 4. Of particular importance in this talk, is the fact th...

Creator:

Sinclair, Christopher (University of Oregon)

Created:

2012-06-18

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

How many large eigenvalues can a graph have? An answer depends on the interpretation of what it means for en eigenvalue to be large. This question and some related problems in extremal algebraic graph theory will be discussed.

Creator:

Mohar, Bojan (Simon Fraser University)

Created:

2012-09-05

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

I will describe recent results (obtained jointly with A. Guionnet P. Wood) concerning perturbations of non-normal random matrices and their stabilization by additive noise. This builds on techniques introduced earlier inthe context of the 'single ring theorem', by Guionnet, Krishnapur, and the speaker.

Creator:

Zeitouni, Ofer (University of Minnesota, Twin Cities)

Created:

2011-09-27

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The intricate structure of many large-scale networkedsystems has attracted the attention of the scientificcommunity, leading to many results attempting to explainthe relationship between the structure of the network and node dynamics.A common approach to study the structure is to use synthetic network models in which structural properties of int...

Creator:

Preciado, Victor Manuel (University of Pennsylvania)

Created:

2012-03-02

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Given a large random matrix A, we consider the following testing problem. Under thenull hypothesis, every entry of A is generated i.i.d. from a distribution P_0. Under the alternative H_1, there is a submatrix indexed by Q, a subset of {1, 2, ... n} such thatthe entries of A in Q X Q are generated instead according to a different law P_1, while ...

Creator:

Deshpande, Yash (Stanford University)

Created:

2015-05-21

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In RMT the hard edge refers to the scaling limits of the minimal eigenvalues for matrices of sample covariance type. In the classical invariant ensembles, the limit distributions are characterized by a Bessel kernel and an associated Painleve III equation (as opposed to the better known Airy kernel and Painleve II descriptions at the 'soft' edge...

Creator:

Rider, Brian (University of Colorado)

Created:

2012-06-20

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We consider several classes of random self-adjoint and unitary operators and investigate their microscopic eigenvalue distribution. We show that some of these operators exhibit a transition in their microscopic eigenvalue distribution, depending on the properties of the corresponding spectral measures. In the case of pure point spectral measures...

Creator:

Stoiciu, Mihai (Williams College)

Created:

2012-06-19

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.