The fluctuation δn of the nth unfolded eigenvalue was recently characterized for the classical Gaussian ensembles of N×N random matrices (GOE, GUE, GSE). It is investigated here for the β-Hermite ensemble as a function of the reciprocal of the temperature β by Monte Carlo simulations. The...

The evolution with β of the distributions of the spacing ‘s’ between nearest-neighbour levels of unfolded spectra of random matrices from the β-Hermite ensemble (β-HE) is investigated by Monte Carlo simulations. The random matrices from the β-HE are real symmetric and tridiagonal where...

Random 2D cellular structures are generated from distributions of spins given by a ferromagnetic Ising model with nearest-neighbour couplings on a square lattice. Topological correlations between pairs of neighbouring cells, are expressed as rational functions of even-number spin correlations,...