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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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