Universality results for zeros of random holomorphic sections
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- by Turgay Bayraktar, Dan Coman and George Marinescu PDF
- Trans. Amer. Math. Soc. 373 (2020), 3765-3791 Request permission
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 Kähler 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 Kähler manifold, we also prove an off-diagonal exponential decay estimate for the Bergman kernels of a sequence of positive line bundles on $X$.References
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Additional Information
- Turgay Bayraktar
- Affiliation: Faculty of Engineering and Natural Sciences, Sabancı University, İstanbul, Turkey
- MR Author ID: 1009679
- Email: tbayraktar@sabanciuniv.edu
- Dan Coman
- Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150
- MR Author ID: 325057
- Email: dcoman@syr.edu
- George Marinescu
- Affiliation: Mathematisches institut, Univerisität zu Köln, Weyertal 86-90, 50931 Köln, Germany; and Institute of Mathematics ‘Simion Stoilow’, Romanian Academy, Bucharest, Romania
- MR Author ID: 819533
- Email: gmarines@math.uni-koeln.de
- Received by editor(s): September 27, 2017
- Received by editor(s) in revised form: October 10, 2018
- Published electronically: March 9, 2020
- Additional Notes: The first author was partially supported by TÜBİTAK 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) - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 3765-3791
- MSC (2010): Primary 32A60, 60D05; Secondary 32L10, 32C20, 32U40, 81Q50
- DOI: https://doi.org/10.1090/tran/7807
- MathSciNet review: 4105509