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.

• Received 12 October 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.3312