Models of intermediate spectral statistics

Based on numerical results it is conjectured that the spectral statistics o f certain pseudointegrable billiards have a special form similar to that of the Anderson model at the transition point. A simple theoretical model whe re such statistics can be obtained analytically is briefly discussed. A few models with similar behavior are considered. In particular, we analyticall y found the eigenvalue statistics of a Poisson-distributed matrix perturbed by a rank one matrix, which is a good model for spectral statistics of a s ingular billiard. [S1063-651X(99)50902-1].