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The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum

M. M. Fogler·B. I. Shklovskii
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Abstract

We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of finding a two-dimensional charge distribution on the interface of a semiconductor heterostructure under the influence of a split gate.

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M. M. Fogler, B. I. Shklovskii. 1994-10-12. The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum. https://doi.org/10.1103/physrevlett.74.3312

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