Related papers: Local eigenvalue statistics of one-dimensional ran…
We will present versions of the Rellich-Kondrachov theorem for pseudo-differential operators acting on localizable Hardy spaces. One of the techniques includes boundedness properties for pseudodifferential operators with symbols in the…
We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain,…
We provide a general formula for the eigenvalue density of large random $N\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zero-mean independent and…
In this work we consider deterministic, symmetric matrices with heavy-tailed noise imposed on entries within a fixed distance $K$ to the diagonal. The most important example is discrete 1d random Schr\"odinger operator defined on…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian Unitary Ensemble. These degeneracies, however, are lifted when the…
Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…
We consider the 1d Schr\"odinger operator with decaying random potential, and study the joint scaling limit of the eigenvalues and the measures associated with the corresponding eigenfunctions which is based on the formulation by…
We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach is to adapt some techniques from one of the recent papers…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
This paper investigates local spectral statistics of singular values for many products of independent large rectangular matrices, sampled from the ensemble of truncated unitary matrices with the invariant Haar measure. Our main contribution…
The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the…
We consider two random matrix ensembles which are relevant for describing critical spectral statistics in systems with multifractal eigenfunction statistics. One of them is the Gaussian non-invariant ensemble which eigenfunction statistics…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…
Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim…
We study higher-order asymptotic expansions of eigenvalues in perturbed transfer operators, of the corresponding eigenfunctions and of the corresponding eigenvectors of the dual operators. In our main result, we give explicit expressions of…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…