Related papers: Probing Band-center Anomaly with the Kernel Polyno…
We show that the tails of the asymptotic density distribution of a quantum wave packet that localizes in the the presence of random or quasiperiodic disorder can be described by the diagonal term of the projection over the eingenstates of…
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for…
We study theoretically Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a random one-dimensional scalar potential. We focus explicitly on the effect of disorder correlations, considering a short-range…
We report a study of a disorder-dependent real-space representation of the quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can…
A new super-symmetric representation for quantum disordered systems is derived. This representation is exact and is dual to that of the nonlinear sigma-model. The new formalism is tested by calculating the distribution of wave function…
The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization.…
We discovered novel Anderson localization behaviors of pseudospin systems in a 1D disordered potential. For a pseudospin-1 system, due to the absence of backscattering under normal incidence and the presence of a conical band structure, the…
In this paper, we propose a kernel method for exact tail asymptotics of a random walk to neighborhoods in the quarter plane. This is a two-dimensional method, which does not require a determination of the unknown generating function(s).…
Non-Bloch band theory serves as a cornerstone for understanding intriguing non-Hermitian phenomena, such as the skin effect and extreme spectral sensitivity to boundary conditions. Yet this theory hinges on translational symmetry and thus…
Until recently, techniques for obtaining lower bounds for kernelization were one of the most sought after tools in the field of parameterized complexity. Now, after a strong influx of techniques, we are in the fortunate situation of having…
The presence of disorder can severely impede wave transport, resulting in the famous Anderson localization. Previous theoretical studies found that Anderson transition can exist in one-dimensional (1D) non-Hermitian disordered rings with…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
We examine the localization properties of the Anderson Hamiltonian with additional off-diagonal disorder using the transfer-matrix method and finite-size scaling. We compute the localization lengths and study the metal-insulator transition…
This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
The interplay between Anderson localization and total internal reflection of electromagnetic waves incident near the critical angle on randomly-stratified dielectric media is investigated theoretically. Using an exact analytical formula for…
The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any rational point $f=2a/\lambda_{E}$, where $a$ is the lattice constant and $\lambda_{E}$ is the de Broglie wavelength. We develop a regular approach to anomalous…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk of the spectrum and near the spectral edge. This…
We study the behavior of two kernel based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), under the nonnull setting that the clean datasets collected from two sensors are modeled…