Related papers: Lifshitz tails for the 1D Bernoulli-Anderson model
We investigate the robustness of unbound states in one-dimensional quasiperiodic models with near-infinitely deep potentials. By constructing a deeper extension of the Liu-Xia model and combining inverse participation ratio (IPR)…
This work studies the tail exponents for the height function of the stationary stochastic six vertex model in the moderate deviations regime. For the upper tail of the height function we find upper and lower bounds of matching order, with a…
We re-examine a lower-tail upper bound for the random variable $$X=\prod_{i=1}^{\infty}\min\left\{\sum_{k=1}^iE_k,1\right\},$$ where $E_1,E_2,\ldots\stackrel{iid}\sim\text{Exp}(1)$. This bound has found use in root-finding and seed-finding…
We show the well-posedness for a large class of degenerate parabolic equations with an additional singularity and mixed Dirichlet-Neumann boundary conditions on bounded Lipschitz domains. The proof is based on an $L^1$-contraction result.…
Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…
We study a broad class of asymmetric copulas introduced by Liebscher (2008) as a combination of multiple - usually symmetric - copulas. The main thrust of the paper is to provide new theoretical properties including exact tail dependence…
Integrable boundary conditions in 1+1 and 2+1 dimensions are discussed from the higher symmetries point of view. Boundary conditions consistent with the discrete Landau-Lifshitz model and infinite 2D Toda lattice are represented.
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
One of the ways to characterize a probability distribution is to show that it is moment-determinate, uniquely determined by knowing all its moments. The uniqueness, in the absolutely continuous case, depends entirely on the behaviour of the…
For differentiable dynamical systems with dominated splittings, we give upper estimates on the measure-theoretic tail entropy in terms of Lyapunov exponents. As our primary application, we verify the upper semi-continuity of metric entropy…
Results of large-scale numerical simulations are reported on the Anderson localization in a two-dimensional square lattice tight-binding model with random flux. Localization lengths, fluctuations of the conductance, and the density of…
We discuss the number-theoretic properties of distributions appearing in physical systems when an observable is a quotient of two independent exponentially weighted integers. The spectral density of ensemble of linear polymer chains…
Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at…
Motivated by the evolution of a population in a slowly varying random environment, we consider the 1D Anderson model on finite volume, with viscosity $ \kappa > 0 $: $$ \partial_{t} u(t,x) = \kappa \Delta u(t,x) + \xi(t, x) u(t,x), \quad…
Let $\mathfrak{q}>2$ be a prime number, $\chi$ a primitive Dirichlet character modulo $\mathfrak{q}$ and $f$ a primitive holomorphic cusp form or a Hecke-Maass cusp form of level $\mathfrak{q}$ and trivial nebentypus. We prove the subconvex…
This is a survey on the intermittent behavior of the parabolic {Anderson} model, which is the Cauchy problem for the heat equation with random potential on the lattice $\Z^d$. We first introduce the model and give heuristic explanations of…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the…
We numerically study the distribution function of the conductance (transmission) in the one-dimensional tight-binding Anderson and periodic-on-average superlattice models in the region of fluctuation states where single parameter scaling is…
We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show that the current can be uniquely reconstructed with Lipschitz…