Related papers: Nodal Sets of Random Eigenfunctions for the Isotro…
This paper considers the asymptotic behaviour of volumes of excursion sets of subordinated Gaussian random fields with (possibly) infinite variance. Actually, we consider integral functionals of such fields and obtain their limiting…
Originally motivated by a stability problem in Fluid Mechanics, we study the spectral and pseudospectral properties of the differential operator $H_\epsilon = -\partial_x^2 + x^2 + i\epsilon^{-1}f(x)$ on $L^2(R)$, where $f$ is a real-valued…
We consider $N\times N$ Hermitian random matrices $H$ consisting of blocks of size $M\geq N^{6/7}$. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from…
We study the number of nodal components (connected components of the set of zeroes) of functions in the ensemble of arithmetic random waves, that is, random eigenfunctions of the Laplacian on the flat $d$-dimensional torus $\mathbb{T}^{d}$…
The simple harmonic oscillator has a well-known normalizable, positive energy, bound state spectrum. We show that degenerate with each such positive energy eigenvalue there is a non-normalizable positive energy eigenstate whose…
We consider non-ergodic class of stationary real harmonizable symmetric $\alpha$-stable processes $X=\left\{X(t):t\in\mathbb{R}\right\}$ with a finite symmetric and absolutely continuous control measure. We refer to its density function as…
In the first part of the paper we study stochastic integrals of a nonrandom function with respect to a nonorthogonal Hilbert noise defined on a semiring of subsets of an arbitrary nonempty set. In the second part we apply this construction…
In the quantization of a rotating rigid body, a {\it top,} one is concerned with the Hamiltonian operator $L_\alpha=\alpha_0^2 L_x^2 + \alpha_1^2 L_y^2 + \alpha_2^2 L_z^2,$ where $\alpha_0 < \alpha_1 <\alpha_2.$ An explicit formula is known…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
We consider a non-homogeneous partially hinged rectangular plate having structural engineering applications. In order to study possible remedies for torsional instability phenomena we consider the gap function as a measure of the torsional…
The oscillation of a Laplacian eigenfunction gives a great deal of information about the manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, an important geometric quantity that is notoriously hard to…
Motivated by recent experimental efforts on three-dimensional semimetals, we investigate the static and dynamic density response of the nodal line semimetal by computing the polarizability for both undoped and doped cases. The nodal line…
These notes present a recent approach to study the high-frequency eigenstates of the Laplacian on compact Riemannian manifolds of negative sectional curvature. The main result is a lower bound on the Kolmogorov-Sinai entropy of the…
We develop a simple algorithm to generate random variables described by densities equaling squared Hermite functions. As an application, we show how to generate a randomly chosen eigenvalue of a matrix from the Gaussian Unitary Ensemble…
In the present paper, fixed trace $\beta$-Hermite ensembles generalizing the fixed trace Gaussian Hermite ensemble are considered. For all $\beta$, we prove the Wigner semicircle law for these ensembles by using two different methods: one…
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the…
Oscillations of local density of states generated by a single scalar impurity potential are calculated for one-dimensional systems with dynamically generated charge or spin gap. At zero temperature the oscillations develop at finite wave…
We derive various sampling functions for multimode homodyne tomography with a single local oscillator. These functions allow us to sample multimode s-parametrized quasidistributions, density matrix elements in Fock basis, and s-ordered…
We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate…
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…