The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way symmetry can be used in the identification of symmetry independent configurations (SICs) is here discussed. First, Pólya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and

It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on Z d admits upper and lower Gaussian estimates.

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