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Level spacings distribution for large random matrices: Gaussian fluctuations. (English) Zbl 0944.60060
From the author’s abstract: “We study the level-spacing distribution for eigenvalues of large $$N\times N$$ matrices from the classical compact groups in the scaling limit when the mean distance between nearest eigenvalues equals 1. Defining by $$\eta_N(s)$$ the number of nearest neigbors spacing greater than $$s$$, we prove functional limit theorem for the process $$(\eta_N(s)-E\eta_N(s))/\sqrt{N}$$, giving weak convergence of this distribution to some Gaussian random process on $$[0,\infty)$$.”
Properties of the limiting process are studied. The article contains an extensive bibliography (40 titles).

MSC:
 60G99 Stochastic processes 15B52 Random matrices (algebraic aspects) 60F17 Functional limit theorems; invariance principles 82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
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