Related papers: Principal Eigenvalue and Landscape Function of the…
We consider Evolution Strategies operating only with isotropic Gaussian mutations on positive quadratic objective functions, and investigate the covariance matrix when constructed out of selected individuals by truncation. We prove that the…
We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local…
We consider square matrices over $\mathbb{C}$ satisfying an identity relating their eigenvalues and the corresponding eigenvectors re-proved and discussed by Denton, Parker, Tao and Zhang, called the eigenvector-eigenvalue identity. We…
We consider invariant matrix models with log-normal (asymptotic) weight. It is known that their eigenvalue distribution is intermediate between Wigner-Dyson and Poissonian, which candidates these models for describing a system intermediate…
We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that…
In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic…
The aim of this paper is to study asymptotic geometric properties almost surely or/and in probability of extreme order statistics of an i.i.d. random field (potential) indexed by sites of multidimensional lattice cube, the volume of which…
Finding the mean of the total number of stationary points for N-dimensional random Gaussian landscapes can be reduced to averaging the absolute value of characteristic polynomial of the corresponding Hessian. First such a reduction is…
The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these…
A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
In this paper, we characterize Probabilistic Principal Component Analysis in Hilbert spaces and demonstrate how the optimal solution admits a representation in dual space. This allows us to develop a generative framework for kernel methods.…
In this paper is studied the problem concerning the angle between two subspaces of arbitrary dimensions in Euclidean space $E_{n}$. It is proven that the angle between two subspaces is equal to the angle between their orthogonal subspaces.…
We consider expansions of eigenvalues and eigenvectors of models of quantum field theory. For a class of models known as generalized spin boson model we prove the existence of asymptotic expansions of the ground state and the ground state…
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
We prove an existence result for the principal-agent problem with adverse selection under general assumptions on preferences and allocation spaces. Instead of assuming that the allocation space is finite-dimensional or compact, we consider…
Given two positive integers $n$ and $k$ and a parameter $t\in (0,1)$, we choose at random a vector subspace $V_{n}\subset \mathbb{C}^{k}\otimes\mathbb{C}^{n}$ of dimension $N\sim tnk$. We show that the set of $k$-tuples of singular values…
The relationship between excess entropy and diffusion is revisited by means of large-scale computer simulation combined to supervised learning approach to determine the excess entropy for the Lennard-Jones potential. Results reveal that it…
We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this…