2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/20414The 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.3 pages; to appear in: "Proceedings of ICSSUR'6, Sixth International Conference on Squeezed States and Uncertainty Relations, 24th May 1999 - 29th May 1999, Universita` degli Studi di Napoli 'Federico II', Naples, Italy", NASA, Greenbelt, Maryland, USA (1999)Statistical Mechanicstext