Open Access
November 2014 Local universality of repulsive particle systems and random matrices
Friedrich Götze, Martin Venker
Ann. Probab. 42(6): 2207-2242 (November 2014). DOI: 10.1214/13-AOP844


We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or determinantal representation, the local correlations in the bulk coincide in the limit of infinitely many particles with those known from random Hermitian matrices; in particular they can be expressed as determinants of the so-called sine kernel. These results may provide an explanation for the appearance of sine kernel correlation statistics in a number of situations which do not have an obvious interpretation in terms of random matrices.


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Friedrich Götze. Martin Venker. "Local universality of repulsive particle systems and random matrices." Ann. Probab. 42 (6) 2207 - 2242, November 2014.


Published: November 2014
First available in Project Euclid: 30 September 2014

zbMATH: 1301.60009
MathSciNet: MR3265167
Digital Object Identifier: 10.1214/13-AOP844

Primary: 15B52 , 60B20
Secondary: 82C22

Keywords: random matrices , repulsive particles , Sine kernel , Universality

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 6 • November 2014
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