Eigenvalues of Random Matrices and Graphs
Random Matrix Theory is at the center of many exciting developments in pure and applied mathematics which touch upon combinatorics, number theory, growth and diffusion processes, quantum chaos as well as probability and statistics. A number of research groups at Arizona study random matrices as a part of their own programs. This includes the groups in Number Theory and Mathematical Physics. In our Analysis group the focus has been on studying the detailed asymptotic behavior of eigenvalue distributions associated to unitarily invariant probability measures on the space of N × N Hermitian matrices as N becomes large. This has led to interesting insights into combinatorial problems related to graphical enumeration on Riemann surfaces, limiting shapes of crystalline surfaces, and the statistical behavior of large random adjacency matrices. In many instances the asymptotic behaviors in these problems can, surprisingly, be described in terms of analytical constructions that arise in integrable systems theory.
Group Members
Graduate Students
Former Graduate Students
- Erin McNicholas, now at Willamette University.
- Jason Newport.
- Virgil Pierce, now at University of Texas Pan American.