Related papers: From exact systems to Riesz bases in the Balian-Lo…
We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a…
This note provides elementary proofs for necessary density conditions for frames and Riesz sequences in the lattice orbit of a discrete series representation that involve the projective stabiliser of the vector. The presented approach…
The roundoff errors in computer simulations of continuous dynamical systems, caused by finiteness of machine arithmetic, can lead to qualitative discrepancies between phase portraits of the resulting spatially discretized systems and the…
We generalize the targeted $\mathcal{B}$-statistic for continuous gravitational waves by modeling the $h_0$-prior as a half-Gaussian distribution with scale parameter $H$. This approach retains analytic tractability for two of the four…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field…
We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a…
We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of…
In this paper, Ostrowski and Brauer type theorems are derived for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic…
The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially…
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
The representer theorem is one of the most important mathematical foundations for regularised learning and kernel methods. Classical formulations of the theorem state sufficient conditions under which a regularisation problem on a Hilbert…
This paper studies quasi Bayesian estimation and uncertainty quantification for an unknown function that is identified by a nonparametric conditional moment restriction. We derive contraction rates for a class of Gaussian process priors.…
We improve the steady-state ab initio laser theory (SALT) of Tureci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities…
We expand our previous study [1] of replicated gauge configurations in lattice SU(Nc) Yang-Mills theory -- employing Bloch's theorem, from condensed-matter physics -- to construct gauge-fixed field configurations on significantly larger…
The Vlasov-Schr\"odinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic/1D quantum steady states in a bounded domain as…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…