Jinho Baik
530 Church Street
Dept. of Mathematics
University of Michigan Ann Arbor, MI 48109-1043
Office: 4071 East Hall
email: lastname at umich edu
Tel: (734) 763-2150
Fax: (734) 763-0937
TTh 11:40-1:00, 3866EH (Room Change!)
Random matrices appear in various places in mathematics and sciences. For example, certain quantities in the theory of quantum gravity, statistics or wireless communications can be modeled as random matrices. In mathematics, certain integrals involving random matrices are generating functions of the numbers of graphs on Riemann surfaces.
More curious fact is that some problems which have no (apparent) matrix structure are also related to random matrices. The most famous example is the non-trivial zeros of Riemann-zeta function. Other examples include random permutations, random Young tableaux, random tiling, growth models and even the bus arrival times at Curenavaca, Mexico. Some computational data on the zeros of zeta function and random permutations can be found at Odlyzko's website.
We will discuss some of the fundamental methods and ideas in random matrix theory developed over the past fifty years, and also discuss the universal nature of the eigenvalue distributions of random matrices. Along the way, various topics in analysis are going to be touched: potential theory of electric charges, integrable systems, trace class operators, Fredholm determinants, Riemann-Hilbert problems, for example. We assume that students are familiar with complex variables and basic functional analysis, but only the very basic probability and combinatorics backgrounds are assumed.
There is no particular textbook, and we will hand out lecture notes. The following books are some references: