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Rescaling Ward Identities in the Random Normal Matrix Model

Ameur, Yacin and Kang, Nam-Gyu and Makarov, Nikolai (2019) Rescaling Ward Identities in the Random Normal Matrix Model. Constructive Approximation, 50 (1). pp. 63-127. ISSN 0176-4276.

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We study spacing distribution for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward’s (or the “rescaled loop”) equation—an identity satisfied by all sequential limits of the rescaled one-point functions.

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Additional Information:© 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Received: 18 September 2017; Revised: 12 February 2018; Accepted: 26 February 2018; First Online: 02 April 2018. Nam-Gyu Kang was supported by Samsung Science and Technology Foundation (SSTF-BA1401-01). Nikolai Makarov was supported by NSF Grant No. 1500821. We thank Alexei Borodin and Misha Sodin for their interest. We also thank Aron Wennman, Seong-Mi Seo, Hee-Joon Tak, and Sungsoo Byun for careful reading and much appreciated help with improving this manuscript.
Funding AgencyGrant Number
Samsung Science and Technology FoundationSSTF-BA1401-01
Subject Keywords:Random normal matrix; Universality; Ward’s equation; Translation invariance
Issue or Number:1
Classification Code:Mathematics Subject Classification: Primary 60B20; Secondary 60G55; 81T40; 30C40; 30D15; 35R09
Record Number:CaltechAUTHORS:20180402-110529752
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Official Citation:Ameur, Y., Kang, NG. & Makarov, N. Constr Approx (2019) 50: 63.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85563
Deposited By: Tony Diaz
Deposited On:02 Apr 2018 18:13
Last Modified:03 Oct 2019 19:32

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