Abstract
We prove that the level spacing distribution at the middle of the spectrum of some one-parameter family of random matrix ensembles has the universal form coinciding with that previously known for several special ensembles. We also discuss some related topics of the random matrix theory.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
WignerE. P., Proc. Cambridge Philos. Soc. 47, 790–795 (1951).
MehtaM. L., Random Matrices, Academic Press, New York, 1967.
FoxD. and KahnP. B., Phys. Rev. B 134, 1151–1155 (1964).
DysonF., J. Math. Phys. 13, 90–97 (1972).
KamienR., PolitzerH. and WiseM., Phys. Rev. Lett. 60, 1995–1998 (1988).
BessisD., ItzyksonC., and ZuberJ., Adv. Appl. Math. 1, 109 (1980).
LubinskyD. S., Strong Asymptotics for Extremal Errors and Polynomials Associated with Erdos-Type Weights, Pitman Research Notes in Math. 202, Longmans, Harlow, 1989.
SzegoG., Orthogonal Polynomials AMS, Providence, 1966.
PasturL., Russ. Math. Surveys 28, 1–58 (1973).
GirkoV., Spectral Theory of Random Matrices Kluwer, Acad. Pubs. Dordrecht, 1990.
PolyaG. and SzegoG., Ausgaben und Lehrsatze aus der Analysis, Springer, Berlin, 1925.
BerezinF., Theor. Math. Phys. 17, 429–435 (1973).
KhorunzhyA., KhoruzhenkoB., PasturL. and ScherbinaM., Phase Transition and Critical Phenomena 15, 73–239 (1992).
MolchanovS., Comm. Math. Phys. 78, 429–446 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pastur, L.A. On the universality of the level spacing distribution for some ensembles of random matrices. Letters in Mathematical Physics 25, 259–265 (1992). https://doi.org/10.1007/BF00398398
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00398398