Three recently suggested random matrix ensembles (RME) are linked together to represent a class of RME with multifractal eigenfunction statistics. The generic form of the two-level correlation function for the case of weak and extremely strong multifractality is suggested.PACS numbers: 72.15.Rn, 05.45+b Random matrix ensembles turn out to be a natural and convenient language to formulate generic statistical properties of energy levels and transmission matrix elements in complex quantum systems. Gaussian random matrix ensembles, first introduced by Wigner and Dyson 1,2 for describing the spectrum of complex nuclei, became very popular in solid state physics as one of the main theoretical tools to study mesoscopic fluctuations 3 in small disordered electronic systems. The success of the random matrix theory (RMT) 2 in mesoscopic physics is due to its extension to the problem of electronic transport based on the Landauer-Büttiker formula 4 and the statistical theory of transmission eigenvalues 5 . Another field where the RMT is exploited very intensively is the problem of the semiclassical approximation in quantum systems whose classical counterpart is chaotic 6 . It turns out 6 that the energy level statistics in true chaotic systems is described by the RMT, in contrast to that in the integrable systems where in most cases it is close to the Poisson statistics.Apparently the nature of the energy level statistics is related to the structure of eigenfunctions, and more precisely, to the overlapping between different eigenfunctions. This is well illustrated by spectral statistics in a system of non-interacting electrons in a random potential which exhibits the Anderson metal-insulator transition with increasing disorder. At small disorder the electron wave functions are extended and essentially structureless. They overlap very well with each other resulting in energy level repulsion characteristic of the Wigner-Dyson statistics. On the other hand in the localized phase electrons are typically localized at different points of the sample, and in the thermodynamic limit where the system size L → ∞ they "do not talk to each other". In this case there is no correlation between eigenvalues, and the energy levels follow the Poisson statistics.The energy level statistics in the critical region near the Anderson transition turns out to be universal and different from both Wigner-Dyson statistics and the Poisson statistics 7,8 . A remarkable feature of the critical level statistics is that the level number variance Σ 2 (N ) = (δN ) 2 = χN is asymptotically linear in the mean number of levelsN ≫ 1 in the energy window. Such a quasiPoisson behavior was first predicted in Ref. [9]. Later the existence of the linear term in Σ 2 (N ) was questioned 8 , since for this term to appear the normalization sum rule should be violated. It has been shown recently 10 that the new qualitative feature responsible for the violation of the sum rule and the existence of the finite "level compressibility" χ is the multifractality of critical w...

We consider an exactly solvable random matrix model related to the random transfer matrix model for disordered conductors. In the conventional random matrix models the spacing distribution of nearest neighbor eigenvalues, when expressed in units of average spacing, has a universal behavior known generally as the Wigner distribution. In contrast, our model has a single parameter, as a function of which the spacing distribution crosses over from a Wigner to a distribution which is increasingly more Poissonlike, a feature common to a wide variety of physical systems including disorder and chaos.

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