The Probability of an Eigenvalue Number Fluctuation in an Interval of a   Random Matrix Spectrum
  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. 
M. M. Fogler and B. I. Shklovskii