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Hole probabilities of random zeros on compact Riemann surfaces

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arxiv 2406.19114 v2 pith:62DI2VMS submitted 2024-06-27 math.CV math.AGmath.PR

Hole probabilities of random zeros on compact Riemann surfaces

Hao Wu , Song-Yan Xie This is my paper
classification math.CV math.AGmath.PR
keywords compactholeprobabilitiesrandomriemannsurfaceszerosconvergence
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We establish a convergence speed estimate for hole probabilities of zeros of random holomorphic sections on compact Riemann surfaces.

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  1. Hole Phenomenon of Gaussian Analytic Functions with Power-exponential Weights

    math.CV 2026-02 reject novelty 6.0

    For every β>0, conditioning a power-exponential Gaussian analytic function to have no zeros in D(0,r) makes the scaled zero measure converge to a limit supported on {|z|=1}∪{|z|≥e^{1/β}}, avoiding {1<|z|<e^{1/β}}.