Random Permutation Matrices
An Investigation of the Number of Eigenvalues
Lying in a Shrinking Interval

Nathaniel Blair-Stahn

Below is a summary of the research I did during Summer 2000 and Spring 2001 at the University of Arizona under the direction of Dr. Kelly Wieand. At the bottom of the page, there is a link to the complete project report, which includes further background information and proofs of the results posted here. Both the summary and the complete report should be accessible to undergraduates who have had some experience with formal proofs.

Project Summary:

• Introduction
• Eigenvalues vs. Independent Points on the Circle
• Major Findings of the Research
  • The Mean Number of Eigenvalues in $I_n$ When $a$ is Rational
  • The Mean When $a$ is Irrational
  
  
• Conclusion
• Bibliography
• About this document ...

Complete Paper:

• Click here for the complete project report in pdf format (~285KB).