| Résume | In 2010, Shiffman and Zelditch established a fundamental result in random complex geometry: the statistics of random zero sets of a single Gaussian holomorphic section obey a Central Limit Theorem (CLT). However, this result was limited to codimension one and smooth statistics. They subsequently posed a natural two-fold generalization: extending the CLT to higher codimensions (common zeros of several sections) and to numerical statistics (volumes of zero sets). In this talk, I will present a complete resolution of this longstanding problem. We prove a universal Central Limit Theorem that holds for intersection currents of k independent Gaussian random holomorphic sections on compact Kähler manifolds. Our result covers both smooth statistics (pairing with test forms) and numerical statistics (volumes in subdomains), despite their distinct fluctuation scales. The proof relies on a delicate Wiener Chaos decomposition and moment analysis via Feynman diagrams, revealing a unified probabilistic structure underlying random complex geometry |
