Hole event for random holomorphic sections on compact Riemann surfaces

Tien-Cuong Dinh, Subhroshekhar Ghosh, Hao Wu

Let $X$ be a compact Riemann surface and $\mathcal{L}$ be a positive line bundle on it. We study the conditional zero expectation of all the holomorphic sections of ${\mathcal{L}}^n$ w…