Asymptotics of hole probability regarding open balls for random sections on compact Riemann surfaces

2025/12/11 by Hao Wu, Wu, Hao
Mathematics · #Geometry and complex manifolds #Point processes and geometric inequalities #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2512.10852

Abstract

We obtain the asymptotic behavior of hole probability for random holomorphic sections on a compact Riemann surface with respect to the hole size.

Citations

• Hole probabilities of random zeros on compact Riemann surfaces
• Hole event for random holomorphic sections on compact Riemann surfaces
• Gaussian holomorphic sections on noncompact complex manifolds
• The forbidden region for random zeros: appearance of quadrature domains
• Point processes, hole events, and large deviations: random complex zeros\n and Coulomb gases
• Gaussian complex zeros on the hole event: the emergence of a forbidden\n region
• Hole probability for zeroes of Gaussian Taylor series with finite radii\n of convergence
• Large deviations for zeros of random polynomials with i.i.d. exponential coefficients
• Hole Probability for Entire Functions represented by Gaussian Taylor Series

Related

• Hole probabilities of random zeros on compact Riemann surfaces
• Hole event for random holomorphic sections on compact Riemann surfaces
• Large deviations for zeros of holomorphic sections on punctured Riemann surfaces
• The Hole Probability for Gaussian Entire Functions
• Hole Probability for Entire Functions represented by Gaussian Taylor Series