Universität zu Köln

Klevtsov, Semyon and Zelditch, Steve (2016). Heat kernel measures on random surfaces. Adv. Theor. Math. Phys., 20 (1). S. 135 - 165. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1095-0753

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Abstract

The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background metric. Under a certain matrix-metric correspondence, each positive definite Hermitian matrix corresponds to a Kahler metric on M. The one and two point functions of the random metric are calculated in a variety of limits as k and t tend to infinity. In the limit when the time t goes to infinity the fluctuations of the random metric around the background metric are the same as the fluctuations of random zeros of holomorphic sections. This is due to the fact that the random zeros form the boundary of the space of Bergman metrics.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klevtsov, Semyon UNSPECIFIED UNSPECIFIED UNSPECIFIED Zelditch, Steve UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-289210
Journal or Publication Title:	Adv. Theor. Math. Phys.
Volume:	20
Number:	1
Page Range:	S. 135 - 165
Date:	2016
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1095-0753
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NUMBER VARIANCE; RANDOM ZEROS Multiple languages Physics, Particles & Fields; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/28921