Edgeworth expansion of the largest eigenvalue distribution function of Gaussian unitary ensemble revisited
Abstract
We derive expansions of the resolvent Rn(x,y;t)=(Qn(x;t)Pn(y;t)−Qn(y;t)Pn(x;t))∕(x−y) of the Hermite kernel Kn at the edge of the spectrum of the finite n Gaussian unitary ensemble (GUEn) and the finite n-expansion of Qn(x;t) and Pn(x;t). Using these large n-expansions, we give another proof of the derivation of an Edgeworth type theorem for the largest eigenvalue distribution function of GUEn. These large n-expansions are essential ingredients in the derivation of our results for Gaussian orthogonal ensemble (GOEn) (Choup, L. N., arXiv:0801.2620v1) where we give explicit n−1∕3 and n−2∕3 correction terms to the limiting GOE Tracy-Widom distribution function.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- March 2008
- DOI:
- 10.1063/1.2873345
- arXiv:
- arXiv:0711.4206
- Bibcode:
- 2008JMP....49c3508C
- Keywords:
-
- Mathematical Physics
- E-Print:
- doi:10.1063/1.2873345