@article{d8e22be1e12444d4a668de817b9cde9b,

title = "Universality results for zeros of random holomorphic sections",

abstract = "In this work we prove a universality result regarding the equidistribution of zeros of random holomorphic sections associated to a sequence of singular Hermitian holomorphic line bundles on a compact K{\"a}hler complex space X. Namely, under mild moment assumptions, we show that the asymptotic distribution of zeros of random holomorphic sections is independent of the choice of the probability measure on the space of holomorphic sections. In the case when X is a compact K{\"a}hler manifold, we also prove an off-diagonal exponential decay estimate for the Bergman kernels of a sequence of positive line bundles on X.",

keywords = "Bergman kernel, Compact normal K{\"a}hler complex space, Fubini-Study current, Singular Hermitian metric, Zeros of random holomorphic sections",

author = "Turgay Bayraktar and Dan Coman and George Marinescu",

note = "Funding Information: Received by the editors September 27, 2017, and, in revised form, October 10, 2018. 2010 Mathematics Subject Classification. Primary 32A60, 60D05; Secondary 32L10, 32C20, 32U40, 81Q50. Key words and phrases. Bergman kernel, Fubini-Study current, singular Hermitian metric, compact normal K{\"a}hler complex space, zeros of random holomorphic sections. The first author was partially supported by T{\"U}BİTAK grants BİDEB 2232/118C006, ARDEB 1001/118F049 and Science Academy, Turkey BAGEP grant. The second author was partially supported by the NSF Grant DMS-1700011. The third author was partially supported by DFG funded project CRC/TRR 191 and gratefully acknowledges the support of Syracuse University, where part of this paper was written. The authors were partially funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative (KPA QM2).",

year = "2020",

month = jun,

doi = "10.1090/tran/7807",

language = "English (US)",

volume = "373",

pages = "3765--3791",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "6",

}