An analogue of the Riemannian Geometry for an ultrametric Cantor set (C, d) is described using the tools of Noncommutative Geometry. Associated with (C, d) is a weighted rooted tree, its Michon treeâ€¦ (More)

We give an overview of the Integer Quantum Hall Effect. We propose a mathematical framework using Non-Commutative Geometry as defined by A. Connes. Within this framework, it is proved that the Hallâ€¦ (More)

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set ofâ€¦ (More)

We develop a mathematical framework allowing to study anomalous transport in homogeneous solids. The main tools characterizing the anomalous transport properties are spectral and diffusion exponentsâ€¦ (More)

By many accounts, the quantum mechanics of disordered media had its origin in Andersonâ€™s ground-breaking and Nobel Prize winning work in 1958 on what is now called Anderson localization. Inâ€¦ (More)

We give a new proof of correlation estimates for arbitrary moments of the resolvent of random SchrÃ¶dinger operators on the lattice that generalizes and extends the correlation estimate of Minami forâ€¦ (More)

Abstract This work proposes a very simple random matrix model, the Flip Matrix Model, liable to approximate the behavior of a two dimensional electron in a weak random potential. Its construction isâ€¦ (More)