Large Deviations for the Fermion Point Process Associated with the Exponential Kernel

For the fermion point process on the whole complex plane associated with the exponential kernel $$e^{z\bar{w}}$$, we show the central limit theorem for the random variable ξ(Dr, the number of points inside the ball Dr of radius r, as r → ∞ and we establish the large deviation principle for the random variables {r−2ξ (Dr), r > 0}.

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