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We consider a family of random matrix ensembles (RME) invariant undersimilarity transformations and described by the probability density $P({\bfH})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of thecorresponding plasma model of eigenvalues is generalized to the case of weakconfining potential, $V(\epsilon)\sim {A\over 2}\ln ^2(\epsilon)$. Theeigenvalue statistics derived from MFT are shown to deviate substantially fromthe classical Wigner-Dyson statistics when $A<1$. By performing systematicMonte Carlo simulations on the plasma model, we compute all the relevantstatistical properties of the RME with weak confinement. For $A_c\approx 0.4$the distribution function of the energy-level spacings (LSDF) of this RMEcoincides in a large energy window with the LSDF of the three dimensionalAnderson model at the metal-insulator transition. For the same $A_c$, thevariance of the number of levels, $\langle n^2\rangle -\langle n\rangle^2$, inan interval containing $\langle n\rangle$ levels on average, grows linearlywith $\langle n\rangle$, and its slope is equal to $0.32 \pm 0.02$, which isconsistent with the value found for the Anderson model at the critical point.Comment: 32 pages, REVTEX 3.0, 10 postscript (uuencoded) figures include

Model for a random-matrix description of the energy-level statistics of disordered systems at the Anderson transition