Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	刘冰萧, 科隆大学
Inviter:	谢松晏
Title:	Introduction to random zeros of holomorphic sections: large deviation and hole probability
Language:	Chinese
Time & Venue:	2024.03.26 15:00-16:30 腾讯会议：116-754-858
Abstract:	For a compact K?hler manifold, by considering the high tensor powers of a prequantum line bundle, Shiffman and Zelditch (1999, CMP) proved the equidistribution of the zeros of random holomorphic sections in the semiclassical limit. Then several generalizations and extensions of this result have been made in different geometric or probabilistic settings. Notably, the large deviation estimates and hole probabilities for the random zeros were also established on compact Hermitian manifolds. In this series of lectures, I will give an introduction to these results and their generalization to the case of noncompact Hermitian manifolds. In the third part, I will explain the large deviation estimates and hole probability of random zeros, specially, to prove these results, we need to introduce the normalized Bergman kernel as the correlation function of the random holomorphic section and prove a near-diagonal asymptotic formula for it.