  The new Theorem on location of maximum of probability density functions of
dimensionless second difference of the three adjacent energy levels for
$N$-dimensional Gaussian orthogonal ensemble GOE($N$), $N$-dimensional Gaussian
unitary ensemble GUE($N$), $N$-dimensional Gaussian symplectic ensemble
GSE($N$), and Poisson ensemble PE, is formulated: {\it The probability density
functions of the dimensionless second difference of the three adjacent energy
levels take on maximum at the origin for the following ensembles: GOE($N$),
GUE($N$), GSE($N$), and PE, where $N \geq 3$.} The notions of {\it level
homogenization with level clustering} and {\it level homogenization with level
repulsion} are introduced.
