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Distribution laws for integrable eigenfunctions

Bernard ShiffmanTatsuya TateSteve Zelditch — 2004

Annales de l’institut Fourier

We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...

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