Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles: Painlevé representations

By M. Dieng. 2004

49 citations recorded by the source corpus.

Author(s): Dieng, Momar | Abstract: We derive Painlev #x27;e--type expressions for the distribution of the $m^{th}$ largest eigenvalue in the Gaussian Orthogonal and Symplectic Ensembles in the edge scaling limit. This work generalizes to general $m$ the $m=1$ results of Tracy and Widom [23]. The results of Johnstone and Soshnikov (see [15], [19]) imply the immediate relevance of our formulas for the $m^{th}$ largest eigenvalue of the appropriate Wishart distribution.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/05fb62902dd8c1bb1349843e6bcac13c4809b7d2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Harold Widom
2. Craig A. Tracy
3. Ivan Corwin
4. Alexei Borodin
5. P. Ferrari
6. Jeremy Quastel

In Statistics and Probability

1. Harold Widom
2. Craig A. Tracy
3. Ivan Corwin
4. Alexei Borodin
5. Neil O'Connell
6. Jinho Baik
7. P. Ferrari
8. Terence Tao

Citations in the corpus

• The Distributions of Random Matrix Theory and their Applications (2009, background): “Chapter 7 of Dieng’s Ph.D. thesis [12] gives MATLAB TM code to evaluate and plot these distributions.”