Related papers: Hopping between Random Locations: Spectrum and Ins…
Transmission probabilities of the scattering problem with a position dependent mass are studied. After sketching the basis of the theory, within the context of the Schr\"{o}dinger equation for spatially varying effective mass, the simplest…
In this paper we develop and apply methods for the spectral analysis of non-self-adjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the…
We study random walks in a random environment on a regular, rooted, coloured tree. The asymptotic behaviour of the walks is classified for ergodicity/transience in terms of the geometric properties of the matrix describing the random…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
A recent approach to the Beck-Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy. We give a complete answer to this question for two natural models:…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal…
Arbitrary waves incident on a solid embedded nanoparticle are studied. The acoustic vibrational frequencies are shown to correspond to the poles of the scattering cross section in the complex frequency plane. The location of the poles is…
Background properties in experimental particle physics are typically estimated using control samples corresponding to large numbers of events. This can provide precise knowledge of average background distributions, but typically does not…
Recently, several papers have been devoted to the analysis of lamplighter random walks, in particular when the underlying graph is the infinite path $\mathbb{Z}$. In the present paper, we develop a spectral analysis for lamplighter random…
By a computer simulation approach we study the scattering of $p$- or $s$-polarized light from a two-dimensional, randomly rough, perfectly conducting surface. The pair of coupled inhomogeneous integral equations for two independent…
In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the…
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminium plate may have an…
It is shown that the contribution of the instantons to the fragmentation of quarks leads to the appearance of a imaginary part in diagrams of quark-quark scattering at large transfer momentum. The imaginary part comes from the analytical…
We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is…
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
We describe extensive computational experiments on spectral properties of random objects - random cubic graphs, random planar triangulations, and Voronoi and Delaunay diagrams of random (uniformly distributed) point sets on the sphere). We…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…