Level-spacing functionP(S) at the mobility edge

We present Lanczos numerical scaling results for the nearest-level-spacing distribution function P(S) favoring a recently proposed random-matrix theory (RMT), which extends the usual RMT appropriate for disordered metals to the Anderson metal-insulator transition. In the three-dimensional (d=3) tight-binding random-matrix ensemble at the mobility edge we obtain a reasonable overall P(S) fit of the form P(S)=BSe^-ASα, where A and B are constants and {α}{}1.31, close to the theoretical value of 2-2/d. We study in more detail the tail of this distribution which is compatible with a lower value of {α}. These results are also shown to hold for the critical number variance 〈[{δ}N(E)]²〉 which obeys the asymptotic law 〈[{δ}N(E)]²〉{∝}〈N(E)〉^2-α.