Introduction to random matrices

• Grant number: 12/13265-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2012
• End date: February 28, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Antonio Lima Santos
• Grantee: Franciele Sampaio dos Santos Safra
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

We will study integrals in matrix spaces, in particular the ensemble of hermitian matrices whose elements are random variables with Gaussian distribution. This ensemble, invariant under unitary transformations, is known as the Gaussian Unitary Ensemble. We will see, introductorily, some of the many applications that matrix integrals have in mathematics and physics. For examples, integrals over the GUE can be used to count maps according to their genus. (AU)