Large dimension expansion of matrix integrals has long been used to study combinatorial objects such as maps, that is graphs sorted by the genus of the surfaces in which they can be properly embedded. In this course, we shall study these expansions. We will first motivate this approach and consider formal expansions. The asymptotics expansions w...
Creator:
Guionnet, Alice (École Normale Supérieure de Lyon)
Created:
2012-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The Harish-Chandra-Itzykson-Zuber integral is a remarkable special function which plays a key role in random matrix theory, where it enters into the description of the spectra of coupled random matrices, Hermitian Wigner matrices, and complex sample covariance matrices. As shown by Guionnet and Zeitouni, the leading asymptotics of the HCIZ integ...
Creator:
Novak, Jonathan (Massachusetts Institute of Technology)
Created:
2012-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This series will highlight the main steps in the approach to universality based on dynamics and comparisons of Green functions. The emphasis will be on the basic steps, not on sharpest results.
Creator:
Zeitouni, Ofer (University of Minnesota, Twin Cities)
Created:
2012-06-25
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.