相关论文: Fluctuations and localization length for random ba…

We consider the Anderson model on a strip. Assuming that potentials have bounded density with considerable tails we get a lower bound for the fluctuations of the logarithm of the Green's function in a finite box. This implies an effective…

We show the eigenvectors of a Gaussian random band matrix are localized when the band width is less than the 1/4 power of the matrix size. Our argument is essentially an optimized version of Schenker's proof of the 1/8 exponent.

We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…

We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova…

Using one-dimensional tight-binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a…

We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W\_N$ deformed by a deterministic diagonal perturbation $D\_N$, around a deterministic equivalent which can be expressed in terms of the free convolution…

We extend methods of Ding and Smart from their breakthrough paper in 2020 which showed Anderson localization for certain random Schr\"odinger operators on $\ell^2(\mathbb{Z}^2)$ via a quantitative unique continuation principle and Wegner…

We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…

We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal…

We show that in any graph, the average length of a flow path in an electrical flow between the endpoints of a random edge is $O(\log^2 n)$. This is a consequence of a more general result which shows that the spectral norm of the entrywise…

We consider the discrete time quantum random walks on a Sierpinski gasket. We study the hitting probability as the level of fractal goes to infinity in terms of their localization exponents $\beta_w$ , total variation exponents $\delta_w$…

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an $n \times n$ matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian…

We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index $\mu=1/2$ and…

We show that the global fluctuations of spectra of GOE and GUE matrices and their principal submatrices executing Dyson's Brownian motion are Gaussian in the limit of large matrix dimensions. For nested submatrices one obtains a limiting…

We report the investigation of conductance fluctuation and shot noise in disordered graphene systems with two kinds of disorder, Anderson type impurities and random dopants. To avoid the brute-force calculation which is time consuming and…

A bijection is given between fixed point free involutions of $\{1,2,...,2N\}$ with maximum decreasing subsequence size $2p$ and two classes of vicious (non-intersecting) random walker configurations confined to the half line lattice points…

We consider a two dimensional magnetic Schroedinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove…

A graph homomorphism between two graphs is a map from the vertex set of one graph to the vertex set of the other graph, that maps edges to edges. In this note we study the range of a uniformly chosen homomorphism from a graph G to the…

We prove that localization near band edges of multi-dimensional ergodic random Schr\"odinger operators with periodic background potential in $L^2(\mathbb{R}^d)$ is universal. By this we mean that localization in its strongest dynamical form…

We performed fluctuation analysis by means of the local scaling dimension for the strength function of the isoscalar (IS) and the isovector (IV) giant quadrupole resonances (GQR) in $^{40}$Ca, where the strength functions are obtained by…