18.338J | Fall 2004 | Graduate
Infinite Random Matrix Theory
Course Description
In this course on the mathematics of infinite random matrices, students will learn about the tools such as the Stieltjes transform and Free Probability used to characterize infinite random matrices.
Learning Resource Types
notes Lecture Notes
Drawing of a non-crossing partition and a crossing partition.
The power of infinite random matrix theory comes from being able to systematically identify and work with non-crossing partitions (as depicted on the left). The figure on the right depicts a crossing partition which becomes important when trying to understand the higher order terms which infinite random matrix theory cannot predict. (Figure by Prof. Alan Edleman.)