Edgeworth expansion of the largest eigenvalue distribution function of Gaussian unitary ensemble revisited
Copyright policy )Edgeworth expansion of the largest eigenvalue distribution function of Gaussian unitary ensemble revisited
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.
- University of Alabama in Huntsville United States
Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics, Gaussian processes, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics, Gaussian processes, Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
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