@article{7d81a8a8ff804d84b8c56667f73a0ca8,
title = "Holomorphic Line Bundles over a Tower of Coverings",
abstract = "We study a tower of normal coverings over a compact K{\"a}hler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we deduce the equidistribution for zero currents of random holomorphic sections. Furthermore, we obtain a variance estimate for those random zero currents, which yields the almost sure convergence under some geometric condition.",
keywords = "Bergman kernel, Equidistribution, Random zero current, Tower of coverings",
author = "Yuan Yuan and Junyan Zhu",
note = "Funding Information: The authors would like to thank Professor Bernard Shiffman and Professor Steve Zelditch for their helpful discussions and Professor Xiaojun Huang for his constant support. The authors also would like to thank the referee for the penetrating comments. Part of the work was done when the first author was visiting Capital Normal University in China and the second author was visiting Syracuse University. They are grateful to both departments for the warm hospitality. Yuan Yuan was Supported in part by National Science Foundation Grant DMS-1412384. Publisher Copyright: {\textcopyright} 2015, Mathematica Josephina, Inc.",
year = "2016",
month = jul,
day = "1",
doi = "10.1007/s12220-015-9617-3",
language = "English (US)",
volume = "26",
pages = "2013--2039",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "3",
}