The Ginibre Ensemble and Gaussian Analytic Functions

Krishnapur, Manjunath and Virag, Balint (2014) The Ginibre Ensemble and Gaussian Analytic Functions. In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES (6). pp. 1441-1464.

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Abstract

We show that as n changes, the characteristic polynomial of the n x n random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to Polya's urn scheme. As a result, we get a random analytic function in the limit, which is given by a mixture of Gaussian analytic functions. This suggests another reason why the zeros of Gaussian analytic functions and the Ginibre ensemble exhibit similar local repulsion, but different global behavior. Our approach gives new explicit formulas for the limiting analytic function.

Item Type:	Journal Article
Publication:	INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Publisher:	OXFORD UNIV PRESS
Additional Information:	Copyright for this article belongs to the OXFORD UNIV PRESS, ENGLAND
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	19 May 2014 05:33
Last Modified:	19 May 2014 05:33
URI:	http://eprints.iisc.ac.in/id/eprint/49107

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