  It is shown that the parametric spectral statistics in the critical random
matrix ensemble with multifractal eigenvector statistics are identical to the
statistics of correlated 1D fermions at finite temperatures. For weak
multifractality the effective temperature of fictitious 1D fermions is
proportional to (1-d_{n})/n, where d_{n} is the fractal dimension found from
the n-th moment of inverse participation ratio. For large energy and parameter
separations the fictitious fermions are described by the Luttinger liquid model
which follows from the Calogero-Sutherland model. The low-temperature
asymptotic form of the two-point equal-parameter spectral correlation function
is found for all energy separations and its relevance for the low temperature
equal-time density correlations in the Calogero-Sutherland model is
conjectured.
