LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES

Götze F, Venker M (2014)
The Annals of Probability 42(6): 2207-2242.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
Universality; sine kernel; repulsive particles; random matrices
Erscheinungsjahr
2014
Zeitschriftentitel
The Annals of Probability
Band
42
Ausgabe
6
Seite(n)
2207-2242
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2701611

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Götze F, Venker M. LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES. The Annals of Probability. 2014;42(6):2207-2242.
Götze, F., & Venker, M. (2014). LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES. The Annals of Probability, 42(6), 2207-2242. doi:10.1214/13-AOP844
Götze, F., and Venker, M. (2014). LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES. The Annals of Probability 42, 2207-2242.
Götze, F., & Venker, M., 2014. LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES. The Annals of Probability, 42(6), p 2207-2242.
F. Götze and M. Venker, “LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES”, The Annals of Probability, vol. 42, 2014, pp. 2207-2242.
Götze, F., Venker, M.: LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES. The Annals of Probability. 42, 2207-2242 (2014).
Götze, Friedrich, and Venker, Martin. “LOCAL UNIVERSALITY OF REPULSIVE PARTICLE SYSTEMS AND RANDOM MATRICES”. The Annals of Probability 42.6 (2014): 2207-2242.