2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57695We study the spectral norm of N-dimensional hermitian random matrices whose entries are zero outside of the band of the width b along the principal diagonal. Inside this band the elements are given by gaussian centered jointly independent random variables with the variance of the order 1/b. We show that if b tends to infinity faster than the third power of log N, then the spectral norm is bounded with probability 1.20 pages, 1 figureMathematical PhysicsProbability15A52text