Prefer a chat interface with context about you and your work?
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 $N\ifmmode\times\else\texttimes\fi{}N$ matrix when this interval contains $s\ensuremath{\ll}N$ 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 …