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

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

1994-10-12

arxiv.org/abs/cond-mat/9410041v1

Phys. Rev. Lett. 74, 3312 (1995)

Physics

Condensed Matter

4 pages, postscript

Scientific paper

10.1103/PhysRevLett.74.3312

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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