Median and mean of the supremum of L-2 normalized random holomorphic fields

作者：Feng Renjie^*; Zelditch Steve

来源：Journal of Functional Analysis, 2014, 266(8): 5085-5107.

DOI：10.1016/j.jfa.2014.02.012

• Random holomorphic sections
• Supremum

We prove that the expected value and median of the supremum of L-2 normalized random holomorphic fields of degree n on m-dimensional Kahler manifolds are asymptotically of order root m log n. There is an exponential concentration of measure of the sup norm around this median value. Prior results only gave the upper bound. The estimates are based on the entropy methods of Dudley and Sudakov combined with a precise analysis of the relevant distance functions and covering numbers using off-diagonal asymptotics of Bergman-Szego kernels. Recent work on the critical value distribution is also used.

• 出版日期2014-4-15
• 单位西北大学