Random matrix ensembles with column/row constraints: I

We analyze statistical properties of a complex system subjected to conditions which manifests through specific constraints on the column/row sum of the matrix elements of its Hermitian operators. The presence of additional constraints besides real-symmetric nature leads to new correlations among their eigenfunctions, hinders a complete delocalization of dynamics and affects the eigenvalues too. The statistical analysis of the latter indicates the presence of a new universality class analogous to that of a special type of Brownian ensemble appearing between Poisson and Gaussian orthogonal ensemble.