Signal Recovery and Universality of Mathematical Systems

Speaker: 
Luis Daniel Abreu - (ARI - Austrian Academy of Sciences)
Date: 
Feb 24 2015 - 3:00pm
Event type: 
IDeAS
Room: 
110 Fine Hall
Abstract: 

In this talk we will discuss applications of universality of mathematical
systems in problems of signal recovering.
Universality is a property shared by several mathematical and physical
systems modelling several interacting particles. Such systems display
chaotic patterns when the number N of particles is low (microscopic
level) However, when N increases, the chaotic patterns start to organize
themselves and, in the asymptotic limit (macroscopic level), the laws
governing their distribution become surprisingly simple and depending on
few parameters. Representative exemples are the Central Limit Theorem and
the asymptotic distribution of eigenvalues of certain random matrices and
determinantal point processes.
We will present two applications of Universality in signal analysis, one in
the approximation of time-variant filters from phaseless information
about their spectrograms, the second in non-parametric estimation of the
power spectral density of stochastic processes.