Random Matrix Theory and the Sixth Painlevé Equation

@inproceedings{Forrester2006RandomMT,
  title={Random Matrix Theory and the Sixth Painlev{\'e} Equation},
  author={Peter J. Forrester and Nicholas S. Witte},
  year={2006}
}
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be τ-functions for Painlevé systems, allowing for the… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 27 references

Studies on the Painlevé equations. I. Sixth Painlevé equation P VI

K Okamoto
Ann. Mat. Pura Appl • 1987
View 6 Excerpts
Highly Influenced

Sur lesleséquations différentielles du second ordre dont l'intégrale générale a ses points critiques fixes

J Malmquist
Arkiv Mat., Astron. Fys • 1922
View 1 Excerpt
Highly Influenced

Log Gases and Random Matrices

P J Forrester
Log Gases and Random Matrices
View 2 Excerpts
Highly Influenced

The Jacobi polynomial ensemble and the Painlevé VI equation

L Haine, J.-P Semengue
The Jacobi polynomial ensemble and the Painlevé VI equation
View 2 Excerpts
Highly Influenced

Similar Papers

Loading similar papers…