Universität zu Köln

Liu, Bingxiao ORCID: 0000-0001-7124-0413 and Zielinski, Dominik ORCID: 0009-0006-9745-419X (2025). Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros. Analysis and Mathematical Physics, 15 (2). pp. 1-61. Springer Nature. ISSN 1664-2368

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Abstract

We present an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.

Item Type:	Article
Creators:	Creators Email ORCID ORCID Put Code Liu, Bingxiao UNSPECIFIED https://orcid.org/0000-0001-7124-0413 UNSPECIFIED Zielinski, Dominik UNSPECIFIED https://orcid.org/0009-0006-9745-419X UNSPECIFIED
URN:	urn:nbn:de:hbz:38-792477
Identification Number:	10.1007/s13324-025-01030-4
Journal or Publication Title:	Analysis and Mathematical Physics
Volume:	15
Number:	2
Page Range:	pp. 1-61
Date:	25 April 2025
Publisher:	Springer Nature
ISSN:	1664-2368
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Data processing Computer science Mathematics
['eprint_fieldname_oa_funders' not defined]:	Publikationsfonds UzK
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79247