# eigenvalues

Tuesday, April 25, 2017 - 9:00am - 10:00am

Chao Yang (Lawrence Berkeley National Laboratory)

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.

Thursday, May 21, 2015 - 3:30pm - 4:20pm

Yash Deshpande (Stanford University)

Given a large random matrix A, we consider the following testing problem. Under the

null 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 that

the entries of A in Q X Q are generated instead according to a different law P_1, while

the other entries are as in the null.

A special case of this problem is the hidden clique problem, which posits to find a clique

null 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 that

the entries of A in Q X Q are generated instead according to a different law P_1, while

the other entries are as in the null.

A special case of this problem is the hidden clique problem, which posits to find a clique

Friday, June 29, 2012 - 11:00am - 12:30pm

Ofer Zeitouni (University of Minnesota, Twin Cities)

Wednesday, June 20, 2012 - 2:00pm - 3:15pm

Brian Rider (University of Colorado)

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). We will show that in the general beta setting these descriptions can be replaced by a limiting (random) differential operator and/or the hitting distributions of a related diffusion process.

Tuesday, June 19, 2012 - 2:00pm - 3:15pm

Mihai Stoiciu (Williams College)

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, the microscopic eigenvalue distribution is Poisson (no correlation).

Monday, June 18, 2012 - 3:30pm - 4:45pm

Christopher Sinclair (University of Oregon)

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 that, when beta is 1 or 4, the marginal densities (vis correlation functions) can be expressed as Pfaffians of antisymmetric matrices formed from a (matrix) kernel.

Wednesday, September 5, 2012 - 3:30pm - 4:30pm

Bojan Mohar (Simon Fraser University)

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.

Friday, March 2, 2012 - 11:30am - 12:00pm

Victor Preciado (University of Pennsylvania)

The intricate structure of many large-scale networked

systems has attracted the attention of the scientific

community, leading to many results attempting to explain

the 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 interest, such as degree distributions,

systems has attracted the attention of the scientific

community, leading to many results attempting to explain

the 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 interest, such as degree distributions,

Tuesday, September 27, 2011 - 3:00pm - 4:00pm

Ofer Zeitouni (University of Minnesota, Twin Cities)

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 in

the context of the single ring theorem, by Guionnet, Krishnapur, and the speaker.

the context of the single ring theorem, by Guionnet, Krishnapur, and the speaker.