We present, in an expository way, an elementary rigorous proof (patterned after an argument of Kirsch-Martinelli) that the Anderson model has Lifschitz tails in very great generality.

We test the property of ultrametricity for the spin-glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to 20(3) spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution, our result contradicts the droplet theory.

In this paper, we consider fractional parabolic equation of the form ∂u ∂t = −(−∆) α 2 u+ uẆ (t, x), where −(−∆)α2 with α ∈ (0, 2] is a fractional Laplacian and Ẇ is a Gaussian noise colored in space and time. The precise moment Lyapunov exponents for the Stratonovich solution and the Skorohod solution are obtained by using a variational inequality and a Feynman-Kac type large deviation result ...

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schrödinger operators, acting on L2(R) ⊗ C , for arbitrary N ≥ 1. We prove that, under suitable assumptions on the Fürstenberg group of these operators, valid on an interval I ⊂ R, they exhibit localization properties on I, both in the spectral and dynamical sense. After looking at the regularity ...

We study the ac-conductivity in linear response theory for the Anderson tight-binding model. We define the electrical acconductivity and calculate the linear-response current at zero temperature for arbitrary Fermi energy. In particular, the Fermi energy may lie in a spectral region where extended states are believed to exist.

The asymmetric infinite-dimensional periodic Anderson model is examined with a quantum Monte Carlo simulation. For small conduction band filling, we find a severe reduction in the Kondo scale, compared to the impurity value, as well as protracted spin screening consistent with some recent controversial photoemission experiments. The Kondo screening drives a ferromagnetic transition when the con...

We give a simple, transparent, and intuitive proof that all eigenvalues of the Anderson model in the region of localization are simple. The Anderson tight binding model is given by the random Hamiltonian Hω = −∆ + Vω on 2(Z), where ∆(x, y) = 1 if |x − y| = 1 and zero otherwise, and the random potential Vω = {Vω(x), x ∈ Zd} consists of independent identically distributed random variables whose c...

When two terms occur together in a document, the probability of a close relationship between them and the document itself is greater if they are in nearby positions. However, ranking functions including term proximity (TP) require larger indexes than traditional document-level indexing, which slows down query processing. Previous studies also show that this technique is not effective for all ty...

Rank breaking is a methodology introduced by Azari Soufiani et al. (2013a) for applying a Generalized Method of Moments (GMM) algorithm to the estimation of parametric ranking models. Breaking takes full rankings and breaks, or splits them up, into counts for pairs of alternatives that occur in particular positions (e.g., first place and second place, second place and third place). GMMs are of ...

We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schrödinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment bound to obtain a new n-level Wegner-type estimate that measures eigenvalue correlations through an upper bound on the probability that a local Hamiltonian ha...