Related papers: Random operators, spectral measures, and local emp…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of countable sofic groups admitting a generating measurable partition with finite entropy; and then David Kerr and Hanfeng Li developed an operator-algebraic…
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The…
We study the approximation of operators acting on probability measures on a product space with prescribed marginal. Let $I$ be a label space endowed with a reference measure $\lambda$, and define $\cal M_\lambda$ as the set of probability…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space $(X,d_X)$. Approximations are constructed in terms…
Since the seminal results by Avellaneda \& Lin it is known that elliptic operators with periodic coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent inspiring work, Armstrong \& Smart proved…
We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost-orthogonality relations. This result is…
Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high-orders of convergence in terms of a…
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…
We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions…
We begin by introducing a class of conditional density estimators based on local polynomial techniques. The estimators are boundary adaptive and easy to implement. We then study the (pointwise and) uniform statistical properties of the…
We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field…
We study perturbations of random dynamical systems whose associated transfer operators admit a uniform spectral gap. We provide a $k^{\text{th}}$-order approximation for the invariant density of the associated random dynamical system. We…
We obtain various new limit theorems for random walks on SL_2(C) under low moment conditions. For non-elementary measures with a finite second moment, we prove a Local Limit Theorem for the norm cocycle, yielding the optimal version of a…
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…
We study the weak convergence (in the high-frequency limit) of the frequency components associated with Gaussian-subordinated, spherical and isotropic random fields. In particular, we provide conditions for asymptotic Gaussianity and we…
Spectral algorithms leverage spectral regularization techniques to analyze and process data, providing a flexible framework for addressing supervised learning problems. To deepen our understanding of their performance in real-world…
Understanding the limiting behavior of eigenvalues of random matrices is the central problem of random matrix theory. Classical limit results are known for many models, and there has been significant recent progress in obtaining more…
In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…