Tracy-Widom GUE law and symplectic invariants
Exactly Solvable and Integrable Systems
2010-11-23 v2 Mathematical Physics
math.MP
Abstract
We establish the relation between two objects: an integrable system related to Painleve II equation, and the symplectic invariants of a certain plane curve \Sigma_{TW} describing the average eigenvalue density of a random hermitian matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This explains directly how the Tracy-Widow law F_{GUE}, governing the distribution of the maximal eigenvalue in hermitian random matrices, can also be recovered from symplectic invariants.
Keywords
Cite
@article{arxiv.1011.1418,
title = {Tracy-Widom GUE law and symplectic invariants},
author = {Gaetan Borot and Bertrand Eynard},
journal= {arXiv preprint arXiv:1011.1418},
year = {2010}
}
Comments
pdfLatex, 36 pages, 1 figure. v2: typos corrected, re-sectioning, a reference added